---
_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: '53319'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The Neumann problem
    for (0.1)$$ \\begin{align}&amp; V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered
    in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where
    $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement
    on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega
    \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big|
    \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}&amp;
    \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}}
    L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau&amp;gt;0$, and
    $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly
    increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to
    \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} &amp;lt;\\infty $ for some $\\lambda
    _0&amp;gt;1$. In the particular case when $p=n\\ge 2$, an additional condition
    on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$
    whenever $b&amp;gt;0$ and $\\alpha&amp;gt;\\frac {(n+2)(n-1)}{2n}$, is identified
    as sufficient to ensure that as a consequence of the above, bounds for theintegrals
    in (0.2) even imply estimates for the spatio-temporal modulus of continuity of
    solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*}
    \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) -
    \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta
    v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb
    {R}}$, $0&amp;lt;D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap
    W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily
    strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu&amp;gt;0$
    excludes blowup in the sense that for all suitably regular nonnegative initial
    data, an associated initial-boundary value problem admits a global bounded classical
    solution.</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
    to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System. <i>International Mathematics Research Notices</i>. 2022;2023(19):16336-16393.
    doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>
  apa: Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System. <i>International Mathematics Research Notices</i>, <i>2023</i>(19),
    16336–16393. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>
  bibtex: '@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity
    in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a
    Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>},
    number={19}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393}
    }'
  chicago: 'Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz
    Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i> 2023,
    no. 19 (2022): 16336–93. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>.'
  ieee: 'M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and
    Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 19,
    pp. 16336–16393, 2022, doi: <a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.'
  mla: Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i>, vol.
    2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.
  short: M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.
date_created: 2024-04-07T12:33:44Z
date_updated: 2024-04-07T12:36:06Z
doi: 10.1093/imrn/rnac286
intvolume: '      2023'
issue: '19'
keyword:
- General Mathematics
language:
- iso: eng
page: 16336-16393
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
  to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
  System
type: journal_article
user_id: '31496'
volume: 2023
year: '2022'
...
---
_id: '63278'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The Neumann problem
    for (0.1)$$ \\begin{align}&amp; V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered
    in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where
    $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement
    on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega
    \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big|
    \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}&amp;
    \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}}
    L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau&amp;gt;0$, and
    $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly
    increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to
    \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} &amp;lt;\\infty $ for some $\\lambda
    _0&amp;gt;1$. In the particular case when $p=n\\ge 2$, an additional condition
    on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$
    whenever $b&amp;gt;0$ and $\\alpha&amp;gt;\\frac {(n+2)(n-1)}{2n}$, is identified
    as sufficient to ensure that as a consequence of the above, bounds for theintegrals
    in (0.2) even imply estimates for the spatio-temporal modulus of continuity of
    solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*}
    \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) -
    \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta
    v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb
    {R}}$, $0&amp;lt;D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap
    W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily
    strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu&amp;gt;0$
    excludes blowup in the sense that for all suitably regular nonnegative initial
    data, an associated initial-boundary value problem admits a global bounded classical
    solution.</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
    to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System. <i>International Mathematics Research Notices</i>. 2022;2023(19):16336-16393.
    doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>
  apa: Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System. <i>International Mathematics Research Notices</i>, <i>2023</i>(19),
    16336–16393. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>
  bibtex: '@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity
    in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a
    Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>},
    number={19}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393}
    }'
  chicago: 'Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz
    Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i> 2023,
    no. 19 (2022): 16336–93. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>.'
  ieee: 'M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and
    Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 19,
    pp. 16336–16393, 2022, doi: <a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.'
  mla: Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i>, vol.
    2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.
  short: M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.
date_created: 2025-12-18T19:15:52Z
date_updated: 2025-12-18T20:11:43Z
doi: 10.1093/imrn/rnac286
intvolume: '      2023'
issue: '19'
language:
- iso: eng
page: 16336-16393
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
  to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
  System
type: journal_article
user_id: '31496'
volume: 2023
year: '2022'
...
---
_id: '31261'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact
    Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector
    bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal
    M$, we give a precise description of those classical (Pollicott–Ruelle) resonant
    states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the
    Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal
    M$. In particular, we show that they are isomorphically mapped by natural pushforwards
    into generalized common eigenspaces of the algebra of invariant differential operators
    $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$
    over $\\mathcal M$. As a consequence of this description, we obtain an exact band
    structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions
    on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau
    }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized
    common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances
    to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections
    of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory
    and Lie theory.</jats:p>"
author:
- first_name: Benjamin
  full_name: Küster, Benjamin
  last_name: Küster
- first_name: Tobias
  full_name: Weich, Tobias
  last_name: Weich
citation:
  ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles
    Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>.
    2021;2021(11):8225-8296. doi:<a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>
  apa: Küster, B., &#38; Weich, T. (2021). Quantum-Classical Correspondence on Associated
    Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research
    Notices</i>, <i>2021</i>(11), 8225–8296. <a href="https://doi.org/10.1093/imrn/rnz068">https://doi.org/10.1093/imrn/rnz068</a>
  bibtex: '@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on
    Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a
    href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>}, number={11},
    journal={International Mathematics Research Notices}, publisher={Oxford University
    Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296}
    }'
  chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence
    on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International
    Mathematics Research Notices</i> 2021, no. 11 (2021): 8225–96. <a href="https://doi.org/10.1093/imrn/rnz068">https://doi.org/10.1093/imrn/rnz068</a>.'
  ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector
    Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research
    Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: <a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>.'
  mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated
    Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research
    Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96,
    doi:<a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>.
  short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021)
    8225–8296.
date_created: 2022-05-17T12:00:36Z
date_updated: 2022-05-25T06:42:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.1093/imrn/rnz068
external_id:
  arxiv:
  - '1710.04625'
intvolume: '      2021'
issue: '11'
keyword:
- General Mathematics
language:
- iso: eng
page: 8225-8296
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally
  Symmetric Spaces
type: journal_article
user_id: '49178'
volume: 2021
year: '2021'
...
---
_id: '37649'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Let $V_k$ denote
    Dunkl’s intertwining operator associated with some root system $R$ and multiplicity
    $k$. For two multiplicities $k, k^{\\prime }$ on $R$, we study the intertwiner
    $V_{k^{\\prime },k} = V_{k^{\\prime }}\\circ V_k^{-1}$ between Dunkl operators
    with multiplicities $k$ and $k^{\\prime }.$ It has been a long-standing conjecture
    that $V_{k^{\\prime },k}$ is positive if $k^{\\prime } \\geq k \\geq 0.$ We disprove
    this conjecture by constructing counterexamples for root system $B_n$. This matter
    is closely related to the existence of Sonine-type integral representations between
    Dunkl kernels and Bessel functions with different multiplicities. In our examples,
    such Sonine formulas do not exist. As a consequence, we obtain necessary conditions
    on Sonine formulas for Heckman–Opdam hypergeometric functions of type $BC_n$ and
    conditions for positive branching coefficients between multivariable Jacobi polynomials.</jats:p>"
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: Michael
  full_name: Voit, Michael
  last_name: Voit
citation:
  ama: Rösler M, Voit M. Sonine Formulas and Intertwining Operators in Dunkl Theory.
    <i>International Mathematics Research Notices</i>. 2021;2021(17):13202-13230.
    doi:<a href="https://doi.org/10.1093/imrn/rnz313">10.1093/imrn/rnz313</a>
  apa: Rösler, M., &#38; Voit, M. (2021). Sonine Formulas and Intertwining Operators
    in Dunkl Theory. <i>International Mathematics Research Notices</i>, <i>2021</i>(17),
    13202–13230. <a href="https://doi.org/10.1093/imrn/rnz313">https://doi.org/10.1093/imrn/rnz313</a>
  bibtex: '@article{Rösler_Voit_2021, title={Sonine Formulas and Intertwining Operators
    in Dunkl Theory}, volume={2021}, DOI={<a href="https://doi.org/10.1093/imrn/rnz313">10.1093/imrn/rnz313</a>},
    number={17}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Rösler, Margit and Voit, Michael}, year={2021},
    pages={13202–13230} }'
  chicago: 'Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators
    in Dunkl Theory.” <i>International Mathematics Research Notices</i> 2021, no.
    17 (2021): 13202–30. <a href="https://doi.org/10.1093/imrn/rnz313">https://doi.org/10.1093/imrn/rnz313</a>.'
  ieee: 'M. Rösler and M. Voit, “Sonine Formulas and Intertwining Operators in Dunkl
    Theory,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 17,
    pp. 13202–13230, 2021, doi: <a href="https://doi.org/10.1093/imrn/rnz313">10.1093/imrn/rnz313</a>.'
  mla: Rösler, Margit, and Michael Voit. “Sonine Formulas and Intertwining Operators
    in Dunkl Theory.” <i>International Mathematics Research Notices</i>, vol. 2021,
    no. 17, Oxford University Press (OUP), 2021, pp. 13202–30, doi:<a href="https://doi.org/10.1093/imrn/rnz313">10.1093/imrn/rnz313</a>.
  short: M. Rösler, M. Voit, International Mathematics Research Notices 2021 (2021)
    13202–13230.
date_created: 2023-01-20T08:50:07Z
date_updated: 2023-01-24T22:16:12Z
doi: 10.1093/imrn/rnz313
intvolume: '      2021'
issue: '17'
keyword:
- General Mathematics
language:
- iso: eng
page: 13202-13230
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Sonine Formulas and Intertwining Operators in Dunkl Theory
type: journal_article
user_id: '37390'
volume: 2021
year: '2021'
...
---
_id: '53416'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact
    Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector
    bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal
    M$, we give a precise description of those classical (Pollicott–Ruelle) resonant
    states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the
    Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal
    M$. In particular, we show that they are isomorphically mapped by natural pushforwards
    into generalized common eigenspaces of the algebra of invariant differential operators
    $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$
    over $\\mathcal M$. As a consequence of this description, we obtain an exact band
    structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions
    on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau
    }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized
    common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances
    to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections
    of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory
    and Lie theory.</jats:p>"
author:
- first_name: Benjamin
  full_name: Küster, Benjamin
  last_name: Küster
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
citation:
  ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles
    Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>.
    2019;2021(11):8225-8296. doi:<a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>
  apa: Küster, B., &#38; Weich, T. (2019). Quantum-Classical Correspondence on Associated
    Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research
    Notices</i>, <i>2021</i>(11), 8225–8296. <a href="https://doi.org/10.1093/imrn/rnz068">https://doi.org/10.1093/imrn/rnz068</a>
  bibtex: '@article{Küster_Weich_2019, title={Quantum-Classical Correspondence on
    Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a
    href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>}, number={11},
    journal={International Mathematics Research Notices}, publisher={Oxford University
    Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2019}, pages={8225–8296}
    }'
  chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence
    on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International
    Mathematics Research Notices</i> 2021, no. 11 (2019): 8225–96. <a href="https://doi.org/10.1093/imrn/rnz068">https://doi.org/10.1093/imrn/rnz068</a>.'
  ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector
    Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research
    Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2019, doi: <a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>.'
  mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated
    Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research
    Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2019, pp. 8225–96,
    doi:<a href="https://doi.org/10.1093/imrn/rnz068">10.1093/imrn/rnz068</a>.
  short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2019)
    8225–8296.
date_created: 2024-04-11T12:33:46Z
date_updated: 2024-04-11T12:36:33Z
department:
- _id: '548'
doi: 10.1093/imrn/rnz068
intvolume: '      2021'
issue: '11'
keyword:
- General Mathematics
language:
- iso: eng
page: 8225-8296
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally
  Symmetric Spaces
type: journal_article
user_id: '70575'
volume: 2021
year: '2019'
...
---
_id: '63325'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>We consider the
    spatially 2D version of the model $$\\begin{equation*} \\qquad\\quad\\left\\{
    \\begin{array}{@{}rcll} n_t + u\\cdot\\nabla n &amp;=&amp; \\Delta n - \\nabla
    \\cdot \\big(nS(x,n,c) \\cdot \\nabla c \\big), \\qquad &amp;\\qquad x\\in \\Omega,
    \\ t&amp;gt;0, \\\\ c_t + u\\cdot \\nabla c &amp;=&amp; \\Delta c - n f(c), \\qquad
    &amp;\\qquad x\\in \\Omega, \\ t&amp;gt;0, \\\\ u_t &amp;=&amp; \\Delta u + \\nabla
    P + n\\nabla\\phi, \\qquad \\nabla\\cdot u=0, \\qquad &amp;\\qquad x\\in \\Omega,
    \\ t&amp;gt;0, \\end{array} \\right. \\qquad \\qquad (\\star) \\end{equation*}$$for
    nutrient taxis processes, possibly interacting with liquid environments. Here
    the particular focus is on the situation when the chemotactic sensitivity $S$
    is not a scalar function but rather attains general values in ${\\mathbb{R}}^{2\\times
    2}$, thus accounting for rotational flux components in accordance with experimental
    findings and recent modeling approaches. Reflecting significant new challenges
    that mainly stem from apparent loss of energy-like structures, especially for
    initial data with large size, the knowledge on ($\\star$) so far seems essentially
    restricted to results on global existence of certain generalized solutions with
    possibly quite poor boundedness and regularity properties; widely unaddressed
    seem aspects related to possible effects of such non-diagonal taxis mechanisms
    on the qualitative solution behavior, especially with regard to the fundamental
    question whether spatial structures may thereby be supported. The present work
    answers the latter in the negative in the following sense: under the assumptions
    that the initial data $(n_0,c_0,u_0)$ and the parameter functions $S$, $f$, and
    $\\phi$ are sufficiently smooth, and that $S$ is bounded and $f$ is positive on
    $(0,\\infty )$ with $f(0)=0$, it is shown that any nontrivial of these solutions
    eventually becomes smooth and satisfies $$\\begin{equation*} n(\\cdot,t)\\to -
    \\int_\\Omega n_0, \\quad c(\\cdot,t)\\to 0 \\quad \\text{and} \\quad u(\\cdot,t)\\to
    0 \\qquad \\text{as} \\ t\\to\\infty, \\end{equation*}$$uniformly with respect
    to $x\\in \\Omega$. By not requiring any smallness condition on the initial data,
    the latter seems new even in the corresponding fluid-free version obtained on
    letting $u\\equiv 0$ in ($\\star$).</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity
    in Nutrient Taxis(-Stokes) Systems? <i>International Mathematics Research Notices</i>.
    2019;2021(11):8106-8152. doi:<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>
  apa: Winkler, M. (2019). Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems? <i>International Mathematics Research
    Notices</i>, <i>2021</i>(11), 8106–8152. <a href="https://doi.org/10.1093/imrn/rnz056">https://doi.org/10.1093/imrn/rnz056</a>
  bibtex: '@article{Winkler_2019, title={Can Rotational Fluxes Impede the Tendency
    Toward Spatial Homogeneity in Nutrient Taxis(-Stokes) Systems?}, volume={2021},
    DOI={<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>}, number={11},
    journal={International Mathematics Research Notices}, publisher={Oxford University
    Press (OUP)}, author={Winkler, Michael}, year={2019}, pages={8106–8152} }'
  chicago: 'Winkler, Michael. “Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems?” <i>International Mathematics
    Research Notices</i> 2021, no. 11 (2019): 8106–52. <a href="https://doi.org/10.1093/imrn/rnz056">https://doi.org/10.1093/imrn/rnz056</a>.'
  ieee: 'M. Winkler, “Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity
    in Nutrient Taxis(-Stokes) Systems?,” <i>International Mathematics Research Notices</i>,
    vol. 2021, no. 11, pp. 8106–8152, 2019, doi: <a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>.'
  mla: Winkler, Michael. “Can Rotational Fluxes Impede the Tendency Toward Spatial
    Homogeneity in Nutrient Taxis(-Stokes) Systems?” <i>International Mathematics
    Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2019,
    pp. 8106–52, doi:<a href="https://doi.org/10.1093/imrn/rnz056">10.1093/imrn/rnz056</a>.
  short: M. Winkler, International Mathematics Research Notices 2021 (2019) 8106–8152.
date_created: 2025-12-18T19:35:55Z
date_updated: 2025-12-18T19:59:29Z
doi: 10.1093/imrn/rnz056
intvolume: '      2021'
issue: '11'
language:
- iso: eng
page: 8106-8152
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity in Nutrient
  Taxis(-Stokes) Systems?
type: journal_article
user_id: '31496'
volume: 2021
year: '2019'
...
---
_id: '66362'
author:
- first_name: Man-Wai
  full_name: Cheung, Man-Wai
  last_name: Cheung
- first_name: Lorenzo
  full_name: Fantini, Lorenzo
  last_name: Fantini
- first_name: Jennifer
  full_name: Park, Jennifer
  last_name: Park
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  ama: Cheung M-W, Fantini L, Park J, Ulirsch M. Faithful Realizability of Tropical
    Curves. <i>International Mathematics Research Notices</i>. 2015;2016(15):4706-4727.
    doi:<a href="https://doi.org/10.1093/imrn/rnv269">10.1093/imrn/rnv269</a>
  apa: Cheung, M.-W., Fantini, L., Park, J., &#38; Ulirsch, M. (2015). Faithful Realizability
    of Tropical Curves. <i>International Mathematics Research Notices</i>, <i>2016</i>(15),
    4706–4727. <a href="https://doi.org/10.1093/imrn/rnv269">https://doi.org/10.1093/imrn/rnv269</a>
  bibtex: '@article{Cheung_Fantini_Park_Ulirsch_2015, title={Faithful Realizability
    of Tropical Curves}, volume={2016}, DOI={<a href="https://doi.org/10.1093/imrn/rnv269">10.1093/imrn/rnv269</a>},
    number={15}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Cheung, Man-Wai and Fantini, Lorenzo and Park,
    Jennifer and Ulirsch, Martin}, year={2015}, pages={4706–4727} }'
  chicago: 'Cheung, Man-Wai, Lorenzo Fantini, Jennifer Park, and Martin Ulirsch. “Faithful
    Realizability of Tropical Curves.” <i>International Mathematics Research Notices</i>
    2016, no. 15 (2015): 4706–27. <a href="https://doi.org/10.1093/imrn/rnv269">https://doi.org/10.1093/imrn/rnv269</a>.'
  ieee: 'M.-W. Cheung, L. Fantini, J. Park, and M. Ulirsch, “Faithful Realizability
    of Tropical Curves,” <i>International Mathematics Research Notices</i>, vol. 2016,
    no. 15, pp. 4706–4727, 2015, doi: <a href="https://doi.org/10.1093/imrn/rnv269">10.1093/imrn/rnv269</a>.'
  mla: Cheung, Man-Wai, et al. “Faithful Realizability of Tropical Curves.” <i>International
    Mathematics Research Notices</i>, vol. 2016, no. 15, Oxford University Press (OUP),
    2015, pp. 4706–27, doi:<a href="https://doi.org/10.1093/imrn/rnv269">10.1093/imrn/rnv269</a>.
  short: M.-W. Cheung, L. Fantini, J. Park, M. Ulirsch, International Mathematics
    Research Notices 2016 (2015) 4706–4727.
date_created: 2026-07-08T08:38:51Z
date_updated: 2026-07-08T08:39:05Z
doi: 10.1093/imrn/rnv269
intvolume: '      2016'
issue: '15'
language:
- iso: eng
page: 4706-4727
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Faithful Realizability of Tropical Curves
type: journal_article
user_id: '82981'
volume: 2016
year: '2015'
...
---
_id: '53185'
article_type: original
author:
- first_name: Fabian
  full_name: Januszewski, Fabian
  id: '81636'
  last_name: Januszewski
citation:
  ama: Januszewski F. On p-adic L-functions for GL(n) × GL (n-1) over totally real
    fields. <i>International Mathematics Research Notices</i>. 2014;2015(17):7884-7949.
    doi:<a href="https://doi.org/10.1093/imrn/rnu181">10.1093/imrn/rnu181</a>
  apa: Januszewski, F. (2014). On p-adic L-functions for GL(n) × GL (n-1) over totally
    real fields. <i>International Mathematics Research Notices</i>, <i>2015</i>(17),
    7884–7949. <a href="https://doi.org/10.1093/imrn/rnu181">https://doi.org/10.1093/imrn/rnu181</a>
  bibtex: '@article{Januszewski_2014, title={On p-adic L-functions for GL(n) × GL
    (n-1) over totally real fields}, volume={2015}, DOI={<a href="https://doi.org/10.1093/imrn/rnu181">10.1093/imrn/rnu181</a>},
    number={17}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Januszewski, Fabian}, year={2014}, pages={7884–7949}
    }'
  chicago: 'Januszewski, Fabian. “On P-Adic L-Functions for GL(n) × GL (n-1) over
    Totally Real Fields.” <i>International Mathematics Research Notices</i> 2015,
    no. 17 (2014): 7884–7949. <a href="https://doi.org/10.1093/imrn/rnu181">https://doi.org/10.1093/imrn/rnu181</a>.'
  ieee: 'F. Januszewski, “On p-adic L-functions for GL(n) × GL (n-1) over totally
    real fields,” <i>International Mathematics Research Notices</i>, vol. 2015, no.
    17, pp. 7884–7949, 2014, doi: <a href="https://doi.org/10.1093/imrn/rnu181">10.1093/imrn/rnu181</a>.'
  mla: Januszewski, Fabian. “On P-Adic L-Functions for GL(n) × GL (n-1) over Totally
    Real Fields.” <i>International Mathematics Research Notices</i>, vol. 2015, no.
    17, Oxford University Press (OUP), 2014, pp. 7884–949, doi:<a href="https://doi.org/10.1093/imrn/rnu181">10.1093/imrn/rnu181</a>.
  short: F. Januszewski, International Mathematics Research Notices 2015 (2014) 7884–7949.
date_created: 2024-04-03T16:48:18Z
date_updated: 2024-04-03T17:12:38Z
doi: 10.1093/imrn/rnu181
extern: '1'
intvolume: '      2015'
issue: '17'
keyword:
- General Mathematics
language:
- iso: eng
page: 7884-7949
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: On p-adic L-functions for GL(n) × GL (n-1) over totally real fields
type: journal_article
user_id: '81636'
volume: 2015
year: '2014'
...
---
_id: '39911'
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: H.
  full_name: Remling, H.
  last_name: Remling
citation:
  ama: Rösler M, Remling H. The Heat Semigroup in the Compact Heckman-Opdam Setting
    and the Segal-Bargmann Transform. <i>International Mathematics Research Notices</i>.
    2011;(18):4200–4225. doi:<a href="https://doi.org/10.1093/imrn/rnq239">10.1093/imrn/rnq239</a>
  apa: Rösler, M., &#38; Remling, H. (2011). The Heat Semigroup in the Compact Heckman-Opdam
    Setting and the Segal-Bargmann Transform. <i>International Mathematics Research
    Notices</i>, <i>18</i>, 4200–4225. <a href="https://doi.org/10.1093/imrn/rnq239">https://doi.org/10.1093/imrn/rnq239</a>
  bibtex: '@article{Rösler_Remling_2011, title={The Heat Semigroup in the Compact
    Heckman-Opdam Setting and the Segal-Bargmann Transform}, DOI={<a href="https://doi.org/10.1093/imrn/rnq239">10.1093/imrn/rnq239</a>},
    number={18}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Rösler, Margit and Remling, H.}, year={2011},
    pages={4200–4225} }'
  chicago: 'Rösler, Margit, and H. Remling. “The Heat Semigroup in the Compact Heckman-Opdam
    Setting and the Segal-Bargmann Transform.” <i>International Mathematics Research
    Notices</i>, no. 18 (2011): 4200–4225. <a href="https://doi.org/10.1093/imrn/rnq239">https://doi.org/10.1093/imrn/rnq239</a>.'
  ieee: 'M. Rösler and H. Remling, “The Heat Semigroup in the Compact Heckman-Opdam
    Setting and the Segal-Bargmann Transform,” <i>International Mathematics Research
    Notices</i>, no. 18, pp. 4200–4225, 2011, doi: <a href="https://doi.org/10.1093/imrn/rnq239">10.1093/imrn/rnq239</a>.'
  mla: Rösler, Margit, and H. Remling. “The Heat Semigroup in the Compact Heckman-Opdam
    Setting and the Segal-Bargmann Transform.” <i>International Mathematics Research
    Notices</i>, no. 18, Oxford University Press (OUP), 2011, pp. 4200–4225, doi:<a
    href="https://doi.org/10.1093/imrn/rnq239">10.1093/imrn/rnq239</a>.
  short: M. Rösler, H. Remling, International Mathematics Research Notices (2011)
    4200–4225.
date_created: 2023-01-25T09:26:07Z
date_updated: 2023-01-26T17:50:05Z
department:
- _id: '555'
doi: 10.1093/imrn/rnq239
extern: '1'
issue: '18'
keyword:
- General Mathematics
language:
- iso: eng
page: 4200–4225
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: The Heat Semigroup in the Compact Heckman-Opdam Setting and the Segal-Bargmann
  Transform
type: journal_article
user_id: '93826'
year: '2011'
...
---
_id: '34885'
abstract:
- lang: eng
  text: We prove that the distribution of the values of the 4-rank of ideal class
    groups of quadratic fields is not affected when it is weighted by a divisor type
    function. We then give several applications concerning a new lower bound of the
    sums of class numbers of real quadratic fields with discriminant less than a bound
    tending to infinity and several questions of P. Sarnak concerning reciprocal geodesics.
author:
- first_name: Étienne
  full_name: Fouvry, Étienne
  last_name: Fouvry
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fouvry É, Klüners J. Weighted Distribution of the 4-rank of Class Groups and
    Applications. <i>International Mathematics Research Notices</i>. 2011;2011(16):3618-3656.
    doi:<a href="https://doi.org/10.1093/imrn/rnq223">10.1093/imrn/rnq223</a>
  apa: Fouvry, É., &#38; Klüners, J. (2011). Weighted Distribution of the 4-rank of
    Class Groups and Applications. <i>International Mathematics Research Notices</i>,
    <i>2011</i>(16), 3618–3656. <a href="https://doi.org/10.1093/imrn/rnq223">https://doi.org/10.1093/imrn/rnq223</a>
  bibtex: '@article{Fouvry_Klüners_2011, title={Weighted Distribution of the 4-rank
    of Class Groups and Applications}, volume={2011}, DOI={<a href="https://doi.org/10.1093/imrn/rnq223">10.1093/imrn/rnq223</a>},
    number={16}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2011},
    pages={3618–3656} }'
  chicago: 'Fouvry, Étienne, and Jürgen Klüners. “Weighted Distribution of the 4-Rank
    of Class Groups and Applications.” <i>International Mathematics Research Notices</i>
    2011, no. 16 (2011): 3618–56. <a href="https://doi.org/10.1093/imrn/rnq223">https://doi.org/10.1093/imrn/rnq223</a>.'
  ieee: 'É. Fouvry and J. Klüners, “Weighted Distribution of the 4-rank of Class Groups
    and Applications,” <i>International Mathematics Research Notices</i>, vol. 2011,
    no. 16, pp. 3618–3656, 2011, doi: <a href="https://doi.org/10.1093/imrn/rnq223">10.1093/imrn/rnq223</a>.'
  mla: Fouvry, Étienne, and Jürgen Klüners. “Weighted Distribution of the 4-Rank of
    Class Groups and Applications.” <i>International Mathematics Research Notices</i>,
    vol. 2011, no. 16, Oxford University Press (OUP), 2011, pp. 3618–56, doi:<a href="https://doi.org/10.1093/imrn/rnq223">10.1093/imrn/rnq223</a>.
  short: É. Fouvry, J. Klüners, International Mathematics Research Notices 2011 (2011)
    3618–3656.
date_created: 2022-12-23T09:08:00Z
date_updated: 2023-03-06T09:07:46Z
department:
- _id: '102'
doi: 10.1093/imrn/rnq223
intvolume: '      2011'
issue: '16'
keyword:
- General Mathematics
language:
- iso: eng
page: 3618-3656
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1687-0247
  - 1073-7928
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Weighted Distribution of the 4-rank of Class Groups and Applications
type: journal_article
user_id: '93826'
volume: 2011
year: '2011'
...
---
_id: '40320'
abstract:
- lang: eng
  text: In this note, a new proof for the positivity of Dunkl's intertwining operator
    in the crystallographic case is given. It is based on an asymptotic relationship
    between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by
    M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials
    and their non-symmetric counterparts.
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: Michael
  full_name: Voit, Michael
  last_name: Voit
citation:
  ama: Rösler M, Voit M. Positivity of Dunkl’s intertwining operator via the trigonometric
    setting. <i>International Mathematics Research Notices</i>. 2004;(63):3379–3389.
    doi:<a href="https://doi.org/10.48550/ARXIV.MATH/0405368">10.48550/ARXIV.MATH/0405368</a>
  apa: Rösler, M., &#38; Voit, M. (2004). Positivity of Dunkl’s intertwining operator
    via the trigonometric setting. <i>International Mathematics Research Notices</i>,
    <i>63</i>, 3379–3389. <a href="https://doi.org/10.48550/ARXIV.MATH/0405368">https://doi.org/10.48550/ARXIV.MATH/0405368</a>
  bibtex: '@article{Rösler_Voit_2004, title={Positivity of Dunkl’s intertwining operator
    via the trigonometric setting}, DOI={<a href="https://doi.org/10.48550/ARXIV.MATH/0405368">10.48550/ARXIV.MATH/0405368</a>},
    number={63}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press}, author={Rösler, Margit and Voit, Michael}, year={2004}, pages={3379–3389}
    }'
  chicago: 'Rösler, Margit, and Michael Voit. “Positivity of Dunkl’s Intertwining
    Operator via the Trigonometric Setting.” <i>International Mathematics Research
    Notices</i>, no. 63 (2004): 3379–3389. <a href="https://doi.org/10.48550/ARXIV.MATH/0405368">https://doi.org/10.48550/ARXIV.MATH/0405368</a>.'
  ieee: 'M. Rösler and M. Voit, “Positivity of Dunkl’s intertwining operator via the
    trigonometric setting,” <i>International Mathematics Research Notices</i>, no.
    63, pp. 3379–3389, 2004, doi: <a href="https://doi.org/10.48550/ARXIV.MATH/0405368">10.48550/ARXIV.MATH/0405368</a>.'
  mla: Rösler, Margit, and Michael Voit. “Positivity of Dunkl’s Intertwining Operator
    via the Trigonometric Setting.” <i>International Mathematics Research Notices</i>,
    no. 63, Oxford University Press, 2004, pp. 3379–3389, doi:<a href="https://doi.org/10.48550/ARXIV.MATH/0405368">10.48550/ARXIV.MATH/0405368</a>.
  short: M. Rösler, M. Voit, International Mathematics Research Notices (2004) 3379–3389.
date_created: 2023-01-26T11:05:33Z
date_updated: 2023-01-26T17:28:09Z
department:
- _id: '555'
doi: 10.48550/ARXIV.MATH/0405368
extern: '1'
issue: '63'
language:
- iso: eng
page: 3379–3389
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press
status: public
title: Positivity of Dunkl's intertwining operator via the trigonometric setting
type: journal_article
user_id: '93826'
year: '2004'
...