---
_id: '65073'
abstract:
- lang: eng
  text: We study the large-time behavior of the continuous-time heat kernel and of
    solutions to the heat equation on homogeneous trees. First, we derive sharp asymptotic
    formulas for the heat kernel as $t\to\infty$. Second, using them, we show that
    solutions with initial data in weighted $\ell^1$ classes, asymptotically factorize
    in $\ell^p$ norms, $p\in[1,\infty]$, as the product of the heat kernel, times
    a $p$-mass function, dependent on the initial condition and $p$. The  $p$-mass
    function is described in terms of boundary averages associated with Busemann functions
    for $p<2$, while for $p\ge 2$, it is expressed through convolution with the ground
    spherical function. For comparison, the case of the integers shows that a single
    constant mass determines the asymptotics of solutions to the heat equation for
    all $p$, emphasizing the influence of the graph geometry on heat diffusion.
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Long-time asymptotics for the heat kernel and for heat equation
    solutions on homogeneous trees. <i>260311232</i>. Published online 2026.
  apa: Papageorgiou, E. (2026). Long-time asymptotics for the heat kernel and for
    heat equation solutions on homogeneous trees. In <i>2603.11232</i>.
  bibtex: '@article{Papageorgiou_2026, title={Long-time asymptotics for the heat kernel
    and for heat equation solutions on homogeneous trees}, journal={2603.11232}, author={Papageorgiou,
    Efthymia}, year={2026} }'
  chicago: Papageorgiou, Efthymia. “Long-Time Asymptotics for the Heat Kernel and
    for Heat Equation Solutions on Homogeneous Trees.” <i>2603.11232</i>, 2026.
  ieee: E. Papageorgiou, “Long-time asymptotics for the heat kernel and for heat equation
    solutions on homogeneous trees,” <i>2603.11232</i>. 2026.
  mla: Papageorgiou, Efthymia. “Long-Time Asymptotics for the Heat Kernel and for
    Heat Equation Solutions on Homogeneous Trees.” <i>2603.11232</i>, 2026.
  short: E. Papageorgiou, 2603.11232 (2026).
date_created: 2026-03-20T17:55:24Z
date_updated: 2026-07-03T12:30:49Z
external_id:
  arxiv:
  - '2603.11232'
language:
- iso: eng
project:
- _id: '357'
  name: 'TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie'
publication: '2603.11232'
status: public
title: Long-time asymptotics for the heat kernel and for heat equation solutions on
  homogeneous trees
type: preprint
user_id: '100325'
year: '2026'
...
---
_id: '65546'
abstract:
- lang: eng
  text: In this paper we study a variant of the uncentred Hardy--Littlewood maximal
    operator on Damek--Ricci spaces in which balls are replaced by suitable half balls.
    Perhaps surprisingly, such modified maximal operator has better boundedness properties
    than the classical one. In particular, it satisfies an $L\log L$ endpoint estimate
    and it is bounded on $L^p$ for every $p$ in $(1,\infty]$.
author:
- first_name: Nikolaos
  full_name: Chalmoukis, Nikolaos
  last_name: Chalmoukis
- first_name: Stefano
  full_name: Meda, Stefano
  last_name: Meda
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
- first_name: Federico
  full_name: Santagati, Federico
  last_name: Santagati
citation:
  ama: Chalmoukis N, Meda S, Papageorgiou E, Santagati F. Uncentred maximal operators
    with respect to half balls on Damek--Ricci spaces. <i>arXiv:260427839</i>. Published
    online 2026.
  apa: Chalmoukis, N., Meda, S., Papageorgiou, E., &#38; Santagati, F. (2026). Uncentred
    maximal operators with respect to half balls on Damek--Ricci spaces. In <i>arXiv:2604.27839</i>.
  bibtex: '@article{Chalmoukis_Meda_Papageorgiou_Santagati_2026, title={Uncentred
    maximal operators with respect to half balls on Damek--Ricci spaces}, journal={arXiv:2604.27839},
    author={Chalmoukis, Nikolaos and Meda, Stefano and Papageorgiou, Efthymia and
    Santagati, Federico}, year={2026} }'
  chicago: Chalmoukis, Nikolaos, Stefano Meda, Efthymia Papageorgiou, and Federico
    Santagati. “Uncentred Maximal Operators with Respect to Half Balls on Damek--Ricci
    Spaces.” <i>ArXiv:2604.27839</i>, 2026.
  ieee: N. Chalmoukis, S. Meda, E. Papageorgiou, and F. Santagati, “Uncentred maximal
    operators with respect to half balls on Damek--Ricci spaces,” <i>arXiv:2604.27839</i>.
    2026.
  mla: Chalmoukis, Nikolaos, et al. “Uncentred Maximal Operators with Respect to Half
    Balls on Damek--Ricci Spaces.” <i>ArXiv:2604.27839</i>, 2026.
  short: N. Chalmoukis, S. Meda, E. Papageorgiou, F. Santagati, ArXiv:2604.27839 (2026).
date_created: 2026-05-03T19:27:27Z
date_updated: 2026-07-03T12:30:33Z
external_id:
  arxiv:
  - '2604.27839'
language:
- iso: eng
project:
- _id: '357'
  name: 'TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie'
publication: arXiv:2604.27839
status: public
title: Uncentred maximal operators with respect to half balls on Damek--Ricci spaces
type: preprint
user_id: '100325'
year: '2026'
...
---
_id: '64266'
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
- first_name: Bartosz
  full_name: Trojan, Bartosz
  last_name: Trojan
citation:
  ama: Papageorgiou E, Trojan B. Mass Functions and Asymptotic Behavior of Caloric
    Functions on Affine Buildings. <i>Mathematische Annalen</i>. 2026;395(30).
  apa: Papageorgiou, E., &#38; Trojan, B. (2026). Mass Functions and Asymptotic Behavior
    of Caloric Functions on Affine Buildings. <i>Mathematische Annalen</i>, <i>395</i>(30).
  bibtex: '@article{Papageorgiou_Trojan_2026, title={Mass Functions and Asymptotic
    Behavior of Caloric Functions on Affine Buildings}, volume={395}, number={30},
    journal={Mathematische Annalen}, author={Papageorgiou, Efthymia and Trojan, Bartosz},
    year={2026} }'
  chicago: Papageorgiou, Efthymia, and Bartosz Trojan. “Mass Functions and Asymptotic
    Behavior of Caloric Functions on Affine Buildings.” <i>Mathematische Annalen</i>
    395, no. 30 (2026).
  ieee: E. Papageorgiou and B. Trojan, “Mass Functions and Asymptotic Behavior of
    Caloric Functions on Affine Buildings,” <i>Mathematische Annalen</i>, vol. 395,
    no. 30, 2026.
  mla: Papageorgiou, Efthymia, and Bartosz Trojan. “Mass Functions and Asymptotic
    Behavior of Caloric Functions on Affine Buildings.” <i>Mathematische Annalen</i>,
    vol. 395, no. 30, 2026.
  short: E. Papageorgiou, B. Trojan, Mathematische Annalen 395 (2026).
date_created: 2026-02-19T11:41:25Z
date_updated: 2026-07-03T12:36:36Z
external_id:
  unknown:
  - ttps://doi.org/10.1007/s00208-026-03453-1
intvolume: '       395'
issue: '30'
language:
- iso: eng
project:
- _id: '357'
  name: 'TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie'
publication: Mathematische Annalen
status: public
title: Mass Functions and Asymptotic Behavior of Caloric Functions on Affine Buildings
type: journal_article
user_id: '100325'
volume: 395
year: '2026'
...
---
_id: '63505'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The main goal
    of this work is to study the $L^{p}$-asymptotic behavior of solutions to the heat
    equation on arbitrary rank Riemannian symmetric spaces of non-compact-type $G/K$
    for non-bi-$K$ invariant initial data. For initial data $u_{0}$ compactly supported
    or in a weighted $L^{1}(G/K)$ space with a weight depending on $p\\in [1, \\infty
    ]$, we introduce a mass function $M_{p}(u_{0})(\\cdot )$, and prove that if $h_{t}$
    is the heat kernel on $G/K$, then $$ \\begin{align*} &amp;\\|h_t\\|_p^{-1}\\,\\|u_0\\ast
    h_t \\, - \\,M_p(u_0)(\\cdot)\\,h_t\\|_p \\rightarrow 0 \\quad \\textrm{as} \\quad
    t\\rightarrow \\infty.\\end{align*} $$ Interestingly, the $L^{p}$ heat concentration
    leads to completely different expressions of the mass function for $1\\leq p &amp;lt;2$
    and $2\\leq p\\leq \\infty $. If we further assume that the initial data are bi-$K$-invariant,
    then our mass function boils down to the constant $\\int _{G/K}u_{0}$ in the case
    $p=1$, and more generally to $\\mathcal{H}{u_{0}}(i\\rho (2/p-1))$ if $1\\leq
    p&amp;lt;2$, and to $\\mathcal{H}{u_{0}}(0)$ if $2\\leq p \\leq \\infty $. Thus,
    we improve upon results by Vázquez, Anker et al., and Naik et al., clarifying
    the nature of the problem.</jats:p>"
article_number: rnaf074
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. <i>L</i>          p Asymptotics for the Heat Equation on Symmetric
    Spaces for Non-symmetric Solutions. <i>International Mathematics Research Notices</i>.
    2025;2025(7). doi:<a href="https://doi.org/10.1093/imrn/rnaf074">10.1093/imrn/rnaf074</a>
  apa: Papageorgiou, E. (2025). <i>L</i>          p Asymptotics for the Heat Equation
    on Symmetric Spaces for Non-symmetric Solutions. <i>International Mathematics
    Research Notices</i>, <i>2025</i>(7), Article rnaf074. <a href="https://doi.org/10.1093/imrn/rnaf074">https://doi.org/10.1093/imrn/rnaf074</a>
  bibtex: '@article{Papageorgiou_2025, title={<i>L</i>          p Asymptotics for
    the Heat Equation on Symmetric Spaces for Non-symmetric Solutions}, volume={2025},
    DOI={<a href="https://doi.org/10.1093/imrn/rnaf074">10.1093/imrn/rnaf074</a>},
    number={7rnaf074}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Papageorgiou, Efthymia}, year={2025} }'
  chicago: Papageorgiou, Efthymia. “<i>L</i>          p Asymptotics for the Heat Equation
    on Symmetric Spaces for Non-Symmetric Solutions.” <i>International Mathematics
    Research Notices</i> 2025, no. 7 (2025). <a href="https://doi.org/10.1093/imrn/rnaf074">https://doi.org/10.1093/imrn/rnaf074</a>.
  ieee: 'E. Papageorgiou, “<i>L</i>          p Asymptotics for the Heat Equation on
    Symmetric Spaces for Non-symmetric Solutions,” <i>International Mathematics Research
    Notices</i>, vol. 2025, no. 7, Art. no. rnaf074, 2025, doi: <a href="https://doi.org/10.1093/imrn/rnaf074">10.1093/imrn/rnaf074</a>.'
  mla: Papageorgiou, Efthymia. “<i>L</i>          p Asymptotics for the Heat Equation
    on Symmetric Spaces for Non-Symmetric Solutions.” <i>International Mathematics
    Research Notices</i>, vol. 2025, no. 7, rnaf074, Oxford University Press (OUP),
    2025, doi:<a href="https://doi.org/10.1093/imrn/rnaf074">10.1093/imrn/rnaf074</a>.
  short: E. Papageorgiou, International Mathematics Research Notices 2025 (2025).
date_created: 2026-01-06T09:45:00Z
date_updated: 2026-07-03T12:36:03Z
doi: 10.1093/imrn/rnaf074
intvolume: '      2025'
issue: '7'
language:
- iso: eng
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: <i>L</i>          p Asymptotics for the Heat Equation on Symmetric Spaces for
  Non-symmetric Solutions
type: journal_article
user_id: '100325'
volume: 2025
year: '2025'
...
---
_id: '64267'
abstract:
- lang: eng
  text: "Let $\\mathbb{H}^n$ be the $n$-dimensional real hyperbolic space, $Δ$ its
    nonnegative Laplace--Beltrami operator whose bottom of the spectrum we denote
    by $λ_{0}$, and $σ\\in (0,1)$.\r\n  The aim of this paper is twofold. On the one
    hand, we determine the Fujita exponent for the fractional heat equation \\[\\partial_{t}
    u + Δ^σu = e^{βt}|u|^{γ-1}u,\\] by proving that nontrivial positive global solutions
    exist if and only if $γ\\geq 1 + β/ λ_{0}^σ$. On the other hand, we prove the
    existence of non-negative, bounded and finite energy solutions of the semilinear
    fractional elliptic equation \\[\r\n  Δ^σ v - λ^σ v - v^γ=0 \\] for $0\\leq λ\\leq
    λ_{0}$ and $1<γ< \\frac{n+2σ}{n-2σ}$. The two problems are known to be connected
    and the latter, aside from its independent interest, is actually instrumental
    to the former.\r\n  \\smallskip\r\n  At the core of our results stands a novel
    fractional Poincaré-type inequality expressed in terms of a new scale of $L^{2}$
    fractional Sobolev spaces, which sharpens those known so far, and which holds
    more generally on Riemannian symmetric spaces of non-compact type. We also establish
    an associated Rellich--Kondrachov-like compact embedding theorem for radial functions,
    along with other related properties."
author:
- first_name: Tommaso
  full_name: Bruno, Tommaso
  last_name: Bruno
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Bruno T, Papageorgiou E. Blow-up exponents and a semilinear elliptic equation
    for the fractional Laplacian on hyperbolic spaces. <i>arXiv:250912349</i>. Published
    online 2025.
  apa: Bruno, T., &#38; Papageorgiou, E. (2025). Blow-up exponents and a semilinear
    elliptic equation for the fractional Laplacian on hyperbolic spaces. In <i>arXiv:2509.12349</i>.
  bibtex: '@article{Bruno_Papageorgiou_2025, title={Blow-up exponents and a semilinear
    elliptic equation for the fractional Laplacian on hyperbolic spaces}, journal={arXiv:2509.12349},
    author={Bruno, Tommaso and Papageorgiou, Efthymia}, year={2025} }'
  chicago: Bruno, Tommaso, and Efthymia Papageorgiou. “Blow-up Exponents and a Semilinear
    Elliptic Equation for the Fractional Laplacian on Hyperbolic Spaces.” <i>ArXiv:2509.12349</i>,
    2025.
  ieee: T. Bruno and E. Papageorgiou, “Blow-up exponents and a semilinear elliptic
    equation for the fractional Laplacian on hyperbolic spaces,” <i>arXiv:2509.12349</i>.
    2025.
  mla: Bruno, Tommaso, and Efthymia Papageorgiou. “Blow-up Exponents and a Semilinear
    Elliptic Equation for the Fractional Laplacian on Hyperbolic Spaces.” <i>ArXiv:2509.12349</i>,
    2025.
  short: T. Bruno, E. Papageorgiou, ArXiv:2509.12349 (2025).
date_created: 2026-02-19T11:42:22Z
date_updated: 2026-07-03T12:31:02Z
external_id:
  arxiv:
  - '2509.12349'
language:
- iso: eng
project:
- _id: '357'
  name: 'TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie'
publication: arXiv:2509.12349
status: public
title: Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian
  on hyperbolic spaces
type: preprint
user_id: '100325'
year: '2025'
...
---
_id: '63500'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>We prove various estimates
    for the asymptotics of counting functions associated to point sets of coherent
    frames and Riesz sequences. The obtained results recover the necessary density
    conditions for coherent frames and Riesz sequences for general unimodular amenable
    groups, while providing more precise estimates under additional localization conditions
    on the coherent system for groups of polynomial growth. \r\n</jats:p>"
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
- first_name: Jordy Timo
  full_name: van Velthoven, Jordy Timo
  last_name: van Velthoven
citation:
  ama: Papageorgiou E, van Velthoven JT. Counting function estimates for coherent
    frames and Riesz sequences. <i>Annali di Matematica Pura ed Applicata (1923 -)</i>.
    2024;204(4):1469-1491. doi:<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>
  apa: Papageorgiou, E., &#38; van Velthoven, J. T. (2024). Counting function estimates
    for coherent frames and Riesz sequences. <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, <i>204</i>(4), 1469–1491. <a href="https://doi.org/10.1007/s10231-024-01535-y">https://doi.org/10.1007/s10231-024-01535-y</a>
  bibtex: '@article{Papageorgiou_van Velthoven_2024, title={Counting function estimates
    for coherent frames and Riesz sequences}, volume={204}, DOI={<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>},
    number={4}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer
    Science and Business Media LLC}, author={Papageorgiou, Efthymia and van Velthoven,
    Jordy Timo}, year={2024}, pages={1469–1491} }'
  chicago: 'Papageorgiou, Efthymia, and Jordy Timo van Velthoven. “Counting Function
    Estimates for Coherent Frames and Riesz Sequences.” <i>Annali Di Matematica Pura
    Ed Applicata (1923 -)</i> 204, no. 4 (2024): 1469–91. <a href="https://doi.org/10.1007/s10231-024-01535-y">https://doi.org/10.1007/s10231-024-01535-y</a>.'
  ieee: 'E. Papageorgiou and J. T. van Velthoven, “Counting function estimates for
    coherent frames and Riesz sequences,” <i>Annali di Matematica Pura ed Applicata
    (1923 -)</i>, vol. 204, no. 4, pp. 1469–1491, 2024, doi: <a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>.'
  mla: Papageorgiou, Efthymia, and Jordy Timo van Velthoven. “Counting Function Estimates
    for Coherent Frames and Riesz Sequences.” <i>Annali Di Matematica Pura Ed Applicata
    (1923 -)</i>, vol. 204, no. 4, Springer Science and Business Media LLC, 2024,
    pp. 1469–91, doi:<a href="https://doi.org/10.1007/s10231-024-01535-y">10.1007/s10231-024-01535-y</a>.
  short: E. Papageorgiou, J.T. van Velthoven, Annali Di Matematica Pura Ed Applicata
    (1923 -) 204 (2024) 1469–1491.
date_created: 2026-01-06T09:33:28Z
date_updated: 2026-07-03T12:37:20Z
doi: 10.1007/s10231-024-01535-y
intvolume: '       204'
issue: '4'
language:
- iso: eng
page: 1469-1491
publication: Annali di Matematica Pura ed Applicata (1923 -)
publication_identifier:
  issn:
  - 0373-3114
  - 1618-1891
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Counting function estimates for coherent frames and Riesz sequences
type: journal_article
user_id: '100325'
volume: 204
year: '2024'
...
---
_id: '53542'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>This work deals with the extension
    problem for the fractional Laplacian on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>
    of noncompact type and of general rank, which gives rise to a family of convolution
    operators, including the Poisson operator. More precisely, motivated by Euclidean
    results for the Poisson semigroup, we study the long-time asymptotic behavior
    of solutions to the extension problem for <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n
    \                   <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    initial data. In the case of the Laplace–Beltrami operator, we show that if the
    initial data are bi-<jats:italic>K</jats:italic>-invariant, then the solution
    to the extension problem behaves asymptotically as the mass times the fundamental
    solution, but this convergence may break down in the non-bi-<jats:italic>K</jats:italic>-invariant
    case. In the second part, we investigate the long-time asymptotic behavior of
    the extension problem associated with the so-called distinguished Laplacian on
    <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>. In this case, we observe
    phenomena which are similar to the Euclidean setting for the Poisson semigroup,
    such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n
    \                   <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    asymptotic convergence without the assumption of bi-<jats:italic>K</jats:italic>-invariance.</jats:p>"
article_number: '34'
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Asymptotic behavior of solutions to the extension problem for
    the fractional Laplacian on noncompact symmetric spaces. <i>Journal of Evolution
    Equations</i>. 2024;24(2). doi:<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>
  apa: Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension
    problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal
    of Evolution Equations</i>, <i>24</i>(2), Article 34. <a href="https://doi.org/10.1007/s00028-024-00959-6">https://doi.org/10.1007/s00028-024-00959-6</a>
  bibtex: '@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to
    the extension problem for the fractional Laplacian on noncompact symmetric spaces},
    volume={24}, DOI={<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>},
    number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science
    and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }'
  chicago: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
    Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal
    of Evolution Equations</i> 24, no. 2 (2024). <a href="https://doi.org/10.1007/s00028-024-00959-6">https://doi.org/10.1007/s00028-024-00959-6</a>.
  ieee: 'E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem
    for the fractional Laplacian on noncompact symmetric spaces,” <i>Journal of Evolution
    Equations</i>, vol. 24, no. 2, Art. no. 34, 2024, doi: <a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>.'
  mla: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
    Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal
    of Evolution Equations</i>, vol. 24, no. 2, 34, Springer Science and Business
    Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>.
  short: E. Papageorgiou, Journal of Evolution Equations 24 (2024).
date_created: 2024-04-17T13:18:30Z
date_updated: 2026-07-03T12:35:54Z
department:
- _id: '555'
doi: 10.1007/s00028-024-00959-6
intvolume: '        24'
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
publication: Journal of Evolution Equations
publication_identifier:
  issn:
  - 1424-3199
  - 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Asymptotic behavior of solutions to the extension problem for the fractional
  Laplacian on noncompact symmetric spaces
type: journal_article
user_id: '100325'
volume: 24
year: '2024'
...
---
_id: '63502'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>Let <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\mu $$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>μ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> be a radial compactly supported distribution
    on a harmonic <jats:italic>NA</jats:italic> group. We prove that the right convolution
    operator <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$c_{\\mu
    }:f \\mapsto f* \\mu $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mi>c</mml:mi>\r\n
    \                     <mml:mi>μ</mml:mi>\r\n                    </mml:msub>\r\n
    \                   <mml:mo>:</mml:mo>\r\n                    <mml:mi>f</mml:mi>\r\n
    \                   <mml:mo>↦</mml:mo>\r\n                    <mml:mi>f</mml:mi>\r\n
    \                   <mml:mrow/>\r\n                    <mml:mo>∗</mml:mo>\r\n
    \                   <mml:mi>μ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula> maps
    the space of smooth <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\mathfrak {v}$$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>v</mml:mi>\r\n
    \               </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>-radial
    functions onto itself if and only if the spherical Fourier transform <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\widetilde{\\mu
    }(\\lambda )$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mover>\r\n                      <mml:mi>μ</mml:mi>\r\n
    \                     <mml:mo>~</mml:mo>\r\n                    </mml:mover>\r\n
    \                   <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n
    \                     <mml:mi>λ</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n
    \                   </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\lambda
    \\in \\mathbb {C}$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>λ</mml:mi>\r\n                    <mml:mo>∈</mml:mo>\r\n
    \                   <mml:mi>C</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, is slowly
    decreasing. As an application, we prove that certain averages over spheres are
    surjective on the space of smooth <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\mathfrak {v}$$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>v</mml:mi>\r\n
    \               </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>-radial
    functions.</jats:p>"
article_number: '7'
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Surjectivity of Convolution Operators on Harmonic NA Groups.
    <i>The Journal of Geometric Analysis</i>. 2024;35(1). doi:<a href="https://doi.org/10.1007/s12220-024-01837-w">10.1007/s12220-024-01837-w</a>
  apa: Papageorgiou, E. (2024). Surjectivity of Convolution Operators on Harmonic
    NA Groups. <i>The Journal of Geometric Analysis</i>, <i>35</i>(1), Article 7.
    <a href="https://doi.org/10.1007/s12220-024-01837-w">https://doi.org/10.1007/s12220-024-01837-w</a>
  bibtex: '@article{Papageorgiou_2024, title={Surjectivity of Convolution Operators
    on Harmonic NA Groups}, volume={35}, DOI={<a href="https://doi.org/10.1007/s12220-024-01837-w">10.1007/s12220-024-01837-w</a>},
    number={17}, journal={The Journal of Geometric Analysis}, publisher={Springer
    Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024}
    }'
  chicago: Papageorgiou, Efthymia. “Surjectivity of Convolution Operators on Harmonic
    NA Groups.” <i>The Journal of Geometric Analysis</i> 35, no. 1 (2024). <a href="https://doi.org/10.1007/s12220-024-01837-w">https://doi.org/10.1007/s12220-024-01837-w</a>.
  ieee: 'E. Papageorgiou, “Surjectivity of Convolution Operators on Harmonic NA Groups,”
    <i>The Journal of Geometric Analysis</i>, vol. 35, no. 1, Art. no. 7, 2024, doi:
    <a href="https://doi.org/10.1007/s12220-024-01837-w">10.1007/s12220-024-01837-w</a>.'
  mla: Papageorgiou, Efthymia. “Surjectivity of Convolution Operators on Harmonic
    NA Groups.” <i>The Journal of Geometric Analysis</i>, vol. 35, no. 1, 7, Springer
    Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s12220-024-01837-w">10.1007/s12220-024-01837-w</a>.
  short: E. Papageorgiou, The Journal of Geometric Analysis 35 (2024).
date_created: 2026-01-06T09:39:35Z
date_updated: 2026-07-03T12:35:33Z
doi: 10.1007/s12220-024-01837-w
intvolume: '        35'
issue: '1'
language:
- iso: eng
publication: The Journal of Geometric Analysis
publication_identifier:
  issn:
  - 1050-6926
  - 1559-002X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Surjectivity of Convolution Operators on Harmonic NA Groups
type: journal_article
user_id: '100325'
volume: 35
year: '2024'
...
---
_id: '63504'
author:
- first_name: Mihail N.
  full_name: Kolountzakis, Mihail N.
  last_name: Kolountzakis
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Kolountzakis MN, Papageorgiou E. Large sets containing no copies of a given
    infinite sequence. <i>Analysis &#38;amp; PDE</i>. 2024;18(1):93-108. doi:<a href="https://doi.org/10.2140/apde.2025.18.93">10.2140/apde.2025.18.93</a>
  apa: Kolountzakis, M. N., &#38; Papageorgiou, E. (2024). Large sets containing no
    copies of a given infinite sequence. <i>Analysis &#38;amp; PDE</i>, <i>18</i>(1),
    93–108. <a href="https://doi.org/10.2140/apde.2025.18.93">https://doi.org/10.2140/apde.2025.18.93</a>
  bibtex: '@article{Kolountzakis_Papageorgiou_2024, title={Large sets containing no
    copies of a given infinite sequence}, volume={18}, DOI={<a href="https://doi.org/10.2140/apde.2025.18.93">10.2140/apde.2025.18.93</a>},
    number={1}, journal={Analysis &#38;amp; PDE}, publisher={Mathematical Sciences
    Publishers}, author={Kolountzakis, Mihail N. and Papageorgiou, Efthymia}, year={2024},
    pages={93–108} }'
  chicago: 'Kolountzakis, Mihail N., and Efthymia Papageorgiou. “Large Sets Containing
    No Copies of a given Infinite Sequence.” <i>Analysis &#38;amp; PDE</i> 18, no.
    1 (2024): 93–108. <a href="https://doi.org/10.2140/apde.2025.18.93">https://doi.org/10.2140/apde.2025.18.93</a>.'
  ieee: 'M. N. Kolountzakis and E. Papageorgiou, “Large sets containing no copies
    of a given infinite sequence,” <i>Analysis &#38;amp; PDE</i>, vol. 18, no. 1,
    pp. 93–108, 2024, doi: <a href="https://doi.org/10.2140/apde.2025.18.93">10.2140/apde.2025.18.93</a>.'
  mla: Kolountzakis, Mihail N., and Efthymia Papageorgiou. “Large Sets Containing
    No Copies of a given Infinite Sequence.” <i>Analysis &#38;amp; PDE</i>, vol. 18,
    no. 1, Mathematical Sciences Publishers, 2024, pp. 93–108, doi:<a href="https://doi.org/10.2140/apde.2025.18.93">10.2140/apde.2025.18.93</a>.
  short: M.N. Kolountzakis, E. Papageorgiou, Analysis &#38;amp; PDE 18 (2024) 93–108.
date_created: 2026-01-06T09:43:35Z
date_updated: 2026-07-03T12:31:35Z
doi: 10.2140/apde.2025.18.93
intvolume: '        18'
issue: '1'
language:
- iso: eng
page: 93-108
publication: Analysis &amp; PDE
publication_identifier:
  issn:
  - 1948-206X
  - 2157-5045
publication_status: published
publisher: Mathematical Sciences Publishers
status: public
title: Large sets containing no copies of a given infinite sequence
type: journal_article
user_id: '100325'
volume: 18
year: '2024'
...
---
_id: '53537'
author:
- first_name: Alexander
  full_name: Grigor'yan, Alexander
  last_name: Grigor'yan
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
- first_name: Hong-Wei
  full_name: Zhang, Hong-Wei
  last_name: Zhang
citation:
  ama: 'Grigor’yan A, Papageorgiou E, Zhang H-W. Asymptotic Behavior of the Heat Semigroup
    on Certain Riemannian Manifolds. In: Alonso Ruiz P, Hinz M, Okoudjou KA, Rogers
    LG, Teplyaev A, eds. <i>From Classical Analysis to Analysis on Fractals. A Tribute
    to Robert Strichartz, Volume 1</i>. Springer International Publishing; 2023. doi:<a
    href="https://doi.org/10.1007/978-3-031-37800-3">10.1007/978-3-031-37800-3</a>'
  apa: Grigor’yan, A., Papageorgiou, E., &#38; Zhang, H.-W. (2023). Asymptotic Behavior
    of the Heat Semigroup on Certain Riemannian Manifolds. In P. Alonso Ruiz, M. Hinz,
    K. A. Okoudjou, L. G. Rogers, &#38; A. Teplyaev (Eds.), <i>From Classical Analysis
    to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 1</i>. Springer
    International Publishing. <a href="https://doi.org/10.1007/978-3-031-37800-3">https://doi.org/10.1007/978-3-031-37800-3</a>
  bibtex: '@inbook{Grigor’yan_Papageorgiou_Zhang_2023, place={Cham}, title={Asymptotic
    Behavior of the Heat Semigroup on Certain Riemannian Manifolds}, DOI={<a href="https://doi.org/10.1007/978-3-031-37800-3">10.1007/978-3-031-37800-3</a>},
    booktitle={From Classical Analysis to Analysis on Fractals. A Tribute to Robert
    Strichartz, Volume 1}, publisher={Springer International Publishing}, author={Grigor’yan,
    Alexander and Papageorgiou, Efthymia and Zhang, Hong-Wei}, editor={Alonso Ruiz,
    Patricia and Hinz, Michael and Okoudjou, Kasso A. and Rogers, Luke G. and Teplyaev,
    Alexander}, year={2023} }'
  chicago: 'Grigor’yan, Alexander, Efthymia Papageorgiou, and Hong-Wei Zhang. “Asymptotic
    Behavior of the Heat Semigroup on Certain Riemannian Manifolds.” In <i>From Classical
    Analysis to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 1</i>,
    edited by Patricia Alonso Ruiz, Michael Hinz, Kasso A. Okoudjou, Luke G. Rogers,
    and Alexander Teplyaev. Cham: Springer International Publishing, 2023. <a href="https://doi.org/10.1007/978-3-031-37800-3">https://doi.org/10.1007/978-3-031-37800-3</a>.'
  ieee: 'A. Grigor’yan, E. Papageorgiou, and H.-W. Zhang, “Asymptotic Behavior of
    the Heat Semigroup on Certain Riemannian Manifolds,” in <i>From Classical Analysis
    to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 1</i>, P. Alonso
    Ruiz, M. Hinz, K. A. Okoudjou, L. G. Rogers, and A. Teplyaev, Eds. Cham: Springer
    International Publishing, 2023.'
  mla: Grigor’yan, Alexander, et al. “Asymptotic Behavior of the Heat Semigroup on
    Certain Riemannian Manifolds.” <i>From Classical Analysis to Analysis on Fractals.
    A Tribute to Robert Strichartz, Volume 1</i>, edited by Patricia Alonso Ruiz et
    al., Springer International Publishing, 2023, doi:<a href="https://doi.org/10.1007/978-3-031-37800-3">10.1007/978-3-031-37800-3</a>.
  short: 'A. Grigor’yan, E. Papageorgiou, H.-W. Zhang, in: P. Alonso Ruiz, M. Hinz,
    K.A. Okoudjou, L.G. Rogers, A. Teplyaev (Eds.), From Classical Analysis to Analysis
    on Fractals. A Tribute to Robert Strichartz, Volume 1, Springer International
    Publishing, Cham, 2023.'
date_created: 2024-04-17T13:11:15Z
date_updated: 2024-04-17T13:14:23Z
doi: 10.1007/978-3-031-37800-3
editor:
- first_name: Patricia
  full_name: Alonso Ruiz, Patricia
  last_name: Alonso Ruiz
- first_name: Michael
  full_name: Hinz, Michael
  last_name: Hinz
- first_name: Kasso A.
  full_name: Okoudjou, Kasso A.
  last_name: Okoudjou
- first_name: Luke G.
  full_name: Rogers, Luke G.
  last_name: Rogers
- first_name: Alexander
  full_name: Teplyaev, Alexander
  last_name: Teplyaev
language:
- iso: eng
place: Cham
publication: From Classical Analysis to Analysis on Fractals. A Tribute to Robert
  Strichartz, Volume 1
publication_identifier:
  isbn:
  - '9783031377990'
  - '9783031378003'
  issn:
  - 2296-5009
  - 2296-5017
publication_status: published
publisher: Springer International Publishing
status: public
title: Asymptotic Behavior of the Heat Semigroup on Certain Riemannian Manifolds
type: book_chapter
user_id: '100325'
year: '2023'
...
---
_id: '53538'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We study harmonic maps from a subset
    of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis
    (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon
    equation and a Bäcklund transformation is introduced, which connects solutions
    of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order
    to construct new harmonic maps to the hyperbolic plane.</jats:p>
author:
- first_name: G.
  full_name: Polychrou, G.
  last_name: Polychrou
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
- first_name: A.
  full_name: Fotiadis, A.
  last_name: Fotiadis
- first_name: C.
  full_name: Daskaloyannis, C.
  last_name: Daskaloyannis
citation:
  ama: Polychrou G, Papageorgiou E, Fotiadis A, Daskaloyannis C. New examples of harmonic
    maps to the hyperbolic plane via Bäcklund transformation. <i>Revista Matemática
    Complutense</i>. Published online 2023. doi:<a href="https://doi.org/10.1007/s13163-023-00476-z">10.1007/s13163-023-00476-z</a>
  apa: Polychrou, G., Papageorgiou, E., Fotiadis, A., &#38; Daskaloyannis, C. (2023).
    New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation.
    <i>Revista Matemática Complutense</i>. <a href="https://doi.org/10.1007/s13163-023-00476-z">https://doi.org/10.1007/s13163-023-00476-z</a>
  bibtex: '@article{Polychrou_Papageorgiou_Fotiadis_Daskaloyannis_2023, title={New
    examples of harmonic maps to the hyperbolic plane via Bäcklund transformation},
    DOI={<a href="https://doi.org/10.1007/s13163-023-00476-z">10.1007/s13163-023-00476-z</a>},
    journal={Revista Matemática Complutense}, publisher={Springer Science and Business
    Media LLC}, author={Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A.
    and Daskaloyannis, C.}, year={2023} }'
  chicago: Polychrou, G., Efthymia Papageorgiou, A. Fotiadis, and C. Daskaloyannis.
    “New Examples of Harmonic Maps to the Hyperbolic Plane via Bäcklund Transformation.”
    <i>Revista Matemática Complutense</i>, 2023. <a href="https://doi.org/10.1007/s13163-023-00476-z">https://doi.org/10.1007/s13163-023-00476-z</a>.
  ieee: 'G. Polychrou, E. Papageorgiou, A. Fotiadis, and C. Daskaloyannis, “New examples
    of harmonic maps to the hyperbolic plane via Bäcklund transformation,” <i>Revista
    Matemática Complutense</i>, 2023, doi: <a href="https://doi.org/10.1007/s13163-023-00476-z">10.1007/s13163-023-00476-z</a>.'
  mla: Polychrou, G., et al. “New Examples of Harmonic Maps to the Hyperbolic Plane
    via Bäcklund Transformation.” <i>Revista Matemática Complutense</i>, Springer
    Science and Business Media LLC, 2023, doi:<a href="https://doi.org/10.1007/s13163-023-00476-z">10.1007/s13163-023-00476-z</a>.
  short: G. Polychrou, E. Papageorgiou, A. Fotiadis, C. Daskaloyannis, Revista Matemática
    Complutense (2023).
date_created: 2024-04-17T13:15:07Z
date_updated: 2024-04-17T13:15:51Z
department:
- _id: '555'
doi: 10.1007/s13163-023-00476-z
keyword:
- General Mathematics
language:
- iso: eng
publication: Revista Matemática Complutense
publication_identifier:
  issn:
  - 1139-1138
  - 1988-2807
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation
type: journal_article
user_id: '100325'
year: '2023'
...
---
_id: '53540'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>This note is concerned with two
    families of operators related to the fractional Laplacian, the first arising from
    the Caffarelli-Silvestre extension problem and the second from the fractional
    heat equation. They both include the Poisson semigroup. We show that on a complete,
    connected, and non-compact Riemannian manifold of non-negative Ricci curvature,
    in both cases, the solution with <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n
    \                 <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    initial data behaves asymptotically as the mass times the fundamental solution.
    Similar long-time convergence results remain valid on more general manifolds satisfying
    the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically
    on hyperbolic space, and more generally on rank one non-compact symmetric spaces:
    we show that for the Poisson semigroup, the convergence to the Poisson kernel
    fails -but remains true under the additional assumption of radial initial data.</jats:p>"
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Large-Time Behavior of Two Families of Operators Related to
    the Fractional Laplacian on Certain Riemannian Manifolds. <i>Potential Analysis</i>.
    Published online 2023. doi:<a href="https://doi.org/10.1007/s11118-023-10109-1">10.1007/s11118-023-10109-1</a>
  apa: Papageorgiou, E. (2023). Large-Time Behavior of Two Families of Operators Related
    to the Fractional Laplacian on Certain Riemannian Manifolds. <i>Potential Analysis</i>.
    <a href="https://doi.org/10.1007/s11118-023-10109-1">https://doi.org/10.1007/s11118-023-10109-1</a>
  bibtex: '@article{Papageorgiou_2023, title={Large-Time Behavior of Two Families
    of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds},
    DOI={<a href="https://doi.org/10.1007/s11118-023-10109-1">10.1007/s11118-023-10109-1</a>},
    journal={Potential Analysis}, publisher={Springer Science and Business Media LLC},
    author={Papageorgiou, Efthymia}, year={2023} }'
  chicago: Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators
    Related to the Fractional Laplacian on Certain Riemannian Manifolds.” <i>Potential
    Analysis</i>, 2023. <a href="https://doi.org/10.1007/s11118-023-10109-1">https://doi.org/10.1007/s11118-023-10109-1</a>.
  ieee: 'E. Papageorgiou, “Large-Time Behavior of Two Families of Operators Related
    to the Fractional Laplacian on Certain Riemannian Manifolds,” <i>Potential Analysis</i>,
    2023, doi: <a href="https://doi.org/10.1007/s11118-023-10109-1">10.1007/s11118-023-10109-1</a>.'
  mla: Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators Related
    to the Fractional Laplacian on Certain Riemannian Manifolds.” <i>Potential Analysis</i>,
    Springer Science and Business Media LLC, 2023, doi:<a href="https://doi.org/10.1007/s11118-023-10109-1">10.1007/s11118-023-10109-1</a>.
  short: E. Papageorgiou, Potential Analysis (2023).
date_created: 2024-04-17T13:17:37Z
date_updated: 2026-07-03T12:37:31Z
department:
- _id: '555'
doi: 10.1007/s11118-023-10109-1
keyword:
- Analysis
language:
- iso: eng
publication: Potential Analysis
publication_identifier:
  issn:
  - 0926-2601
  - 1572-929X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-Time Behavior of Two Families of Operators Related to the Fractional
  Laplacian on Certain Riemannian Manifolds
type: journal_article
user_id: '100325'
year: '2023'
...
---
_id: '53539'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>The infinite Brownian loop on a
    Riemannian manifold is the limit in distribution of the Brownian bridge of length
    <jats:italic>T</jats:italic> around a fixed origin when <jats:inline-formula><jats:alternatives><jats:tex-math>$$T
    \\rightarrow +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>T</mml:mi>\r\n                  <mml:mo>→</mml:mo>\r\n
    \                 <mml:mo>+</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n
    \               </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>.
    The aim of this note is to study its long-time asymptotics on Riemannian symmetric
    spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic> of noncompact
    type and of general rank. This amounts to the behavior of solutions to the heat
    equation subject to the Doob transform induced by the ground spherical function.
    Unlike the standard Brownian motion, we observe in this case phenomena which are
    similar to the Euclidean setting, namely <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n
    \                 <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    asymptotic convergence without requiring bi-<jats:italic>K</jats:italic>-invariance
    for initial data, and strong <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\infty
    }$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:msup>\r\n                  <mml:mi>L</mml:mi>\r\n                  <mml:mi>∞</mml:mi>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    convergence.</jats:p>"
author:
- first_name: Efthymia
  full_name: Papageorgiou, Efthymia
  id: '100325'
  last_name: Papageorgiou
citation:
  ama: Papageorgiou E. Asymptotics for the infinite Brownian loop on noncompact symmetric
    spaces. <i>Journal of Elliptic and Parabolic Equations</i>. Published online 2023.
    doi:<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>
  apa: Papageorgiou, E. (2023). Asymptotics for the infinite Brownian loop on noncompact
    symmetric spaces. <i>Journal of Elliptic and Parabolic Equations</i>. <a href="https://doi.org/10.1007/s41808-023-00250-8">https://doi.org/10.1007/s41808-023-00250-8</a>
  bibtex: '@article{Papageorgiou_2023, title={Asymptotics for the infinite Brownian
    loop on noncompact symmetric spaces}, DOI={<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>},
    journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer Science
    and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2023} }'
  chicago: Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on
    Noncompact Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>,
    2023. <a href="https://doi.org/10.1007/s41808-023-00250-8">https://doi.org/10.1007/s41808-023-00250-8</a>.
  ieee: 'E. Papageorgiou, “Asymptotics for the infinite Brownian loop on noncompact
    symmetric spaces,” <i>Journal of Elliptic and Parabolic Equations</i>, 2023, doi:
    <a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>.'
  mla: Papageorgiou, Efthymia. “Asymptotics for the Infinite Brownian Loop on Noncompact
    Symmetric Spaces.” <i>Journal of Elliptic and Parabolic Equations</i>, Springer
    Science and Business Media LLC, 2023, doi:<a href="https://doi.org/10.1007/s41808-023-00250-8">10.1007/s41808-023-00250-8</a>.
  short: E. Papageorgiou, Journal of Elliptic and Parabolic Equations (2023).
date_created: 2024-04-17T13:16:39Z
date_updated: 2026-07-03T12:36:17Z
department:
- _id: '555'
doi: 10.1007/s41808-023-00250-8
keyword:
- Applied Mathematics
- Numerical Analysis
- Analysis
language:
- iso: eng
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
  issn:
  - 2296-9020
  - 2296-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Asymptotics for the infinite Brownian loop on noncompact symmetric spaces
type: journal_article
user_id: '100325'
year: '2023'
...