---
_id: '54820'
abstract:
- lang: eng
  text: "We study the asymptotic behaviour of Bessel functions associated of root\r\nsystems
    of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the\r\nrank $n$
    tends to infinity. In both cases, we characterize the possible limit\r\nfunctions
    and the Vershik-Kerov type sequences of spectral parameters for which\r\nsuch
    limits exist. In the type $A$ case, this gives a new and very natural\r\napproach
    to recent results by Assiotis and Najnudel in the context of\r\n$\\beta$-ensembles
    in random matrix theory. These results generalize known facts\r\nabout the approximation
    of the (positive-definite) Olshanski spherical\r\nfunctions of the space of infinite-dimensional
    Hermitian matrices over $\\mathbb\r\nF = \\mathbb R, \\mathbb C, \\mathbb H$ (with
    the action of the associated\r\ninfinite unitary group) by spherical functions
    of finite-dimensional spaces of\r\nHermitian matrices. In the type B case, our
    results include asymptotic results\r\nfor the spherical functions associated with
    the Cartan motion groups of\r\nnon-compact Grassmannians as the rank goes to infinity,
    and a classification of\r\nthe Olshanski spherical functions of the associated
    inductive limits."
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Brennecken D, Rösler M. Limits of Bessel functions for root systems as the
    rank tends to  infinity. <i>Indagationes Mathematicae</i>. Published online 2024.
    doi:<a href="https://doi.org/10.1016/j.indag.2024.05.004">10.1016/j.indag.2024.05.004</a>
  apa: Brennecken, D., &#38; Rösler, M. (2024). Limits of Bessel functions for root
    systems as the rank tends to  infinity. <i>Indagationes Mathematicae</i>. <a href="https://doi.org/10.1016/j.indag.2024.05.004">https://doi.org/10.1016/j.indag.2024.05.004</a>
  bibtex: '@article{Brennecken_Rösler_2024, title={Limits of Bessel functions for
    root systems as the rank tends to  infinity}, DOI={<a href="https://doi.org/10.1016/j.indag.2024.05.004">10.1016/j.indag.2024.05.004</a>},
    journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Brennecken,
    Dominik and Rösler, Margit}, year={2024} }'
  chicago: Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for
    Root Systems as the Rank Tends to  Infinity.” <i>Indagationes Mathematicae</i>,
    2024. <a href="https://doi.org/10.1016/j.indag.2024.05.004">https://doi.org/10.1016/j.indag.2024.05.004</a>.
  ieee: 'D. Brennecken and M. Rösler, “Limits of Bessel functions for root systems
    as the rank tends to  infinity,” <i>Indagationes Mathematicae</i>, 2024, doi:
    <a href="https://doi.org/10.1016/j.indag.2024.05.004">10.1016/j.indag.2024.05.004</a>.'
  mla: Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root
    Systems as the Rank Tends to  Infinity.” <i>Indagationes Mathematicae</i>, Elsevier,
    2024, doi:<a href="https://doi.org/10.1016/j.indag.2024.05.004">10.1016/j.indag.2024.05.004</a>.
  short: D. Brennecken, M. Rösler, Indagationes Mathematicae (2024).
date_created: 2024-06-19T08:46:08Z
date_updated: 2024-07-15T09:09:55Z
doi: 10.1016/j.indag.2024.05.004
language:
- iso: eng
publication: Indagationes Mathematicae
publication_status: epub_ahead
publisher: Elsevier
status: public
title: Limits of Bessel functions for root systems as the rank tends to  infinity
type: journal_article
user_id: '82981'
year: '2024'
...
---
_id: '53300'
article_number: '128125'
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
citation:
  ama: Brennecken D. Hankel transform, K-Bessel functions and zeta distributions in
    the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>. 2024;535(2).
    doi:<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>
  apa: Brennecken, D. (2024). Hankel transform, K-Bessel functions and zeta distributions
    in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>,
    <i>535</i>(2), Article 128125. <a href="https://doi.org/10.1016/j.jmaa.2024.128125">https://doi.org/10.1016/j.jmaa.2024.128125</a>
  bibtex: '@article{Brennecken_2024, title={Hankel transform, K-Bessel functions and
    zeta distributions in the Dunkl setting}, volume={535}, DOI={<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>},
    number={2128125}, journal={Journal of Mathematical Analysis and Applications},
    publisher={Elsevier BV}, author={Brennecken, Dominik}, year={2024} }'
  chicago: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
    in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>
    535, no. 2 (2024). <a href="https://doi.org/10.1016/j.jmaa.2024.128125">https://doi.org/10.1016/j.jmaa.2024.128125</a>.
  ieee: 'D. Brennecken, “Hankel transform, K-Bessel functions and zeta distributions
    in the Dunkl setting,” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 535, no. 2, Art. no. 128125, 2024, doi: <a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>.'
  mla: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
    in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 535, no. 2, 128125, Elsevier BV, 2024, doi:<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>.
  short: D. Brennecken, Journal of Mathematical Analysis and Applications 535 (2024).
date_created: 2024-04-05T13:55:33Z
date_updated: 2024-09-03T14:40:46Z
department:
- _id: '555'
doi: 10.1016/j.jmaa.2024.128125
intvolume: '       535'
issue: '2'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
  issn:
  - 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting
type: journal_article
user_id: '55911'
volume: 535
year: '2024'
...
---
_id: '56001'
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: 'Brennecken D, Rösler M. The Laplace transform in Dunkl theory. In: Chatzakou
    M, Ruzhansky M, Stoeva D, eds. <i>Women in Analysis and PDE</i>. Vol 5. Trends
    in Mathematics: Research Perspectives Ghent Analysis and PDE Cente. Birkhäuser
    Cham; 2024:425.'
  apa: Brennecken, D., &#38; Rösler, M. (2024). The Laplace transform in Dunkl theory.
    In M. Chatzakou, M. Ruzhansky, &#38; D. Stoeva (Eds.), <i>Women in Analysis and
    PDE</i> (Vol. 5, p. 425). Birkhäuser Cham.
  bibtex: '@inbook{Brennecken_Rösler_2024, series={Trends in Mathematics: Research
    Perspectives Ghent Analysis and PDE Cente}, title={The Laplace transform in Dunkl
    theory}, volume={5}, booktitle={Women in Analysis and PDE}, publisher={Birkhäuser
    Cham}, author={Brennecken, Dominik and Rösler, Margit}, editor={Chatzakou, Marianna
    and Ruzhansky, Michael and Stoeva, Diana}, year={2024}, pages={425}, collection={Trends
    in Mathematics: Research Perspectives Ghent Analysis and PDE Cente} }'
  chicago: 'Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl
    Theory.” In <i>Women in Analysis and PDE</i>, edited by Marianna Chatzakou, Michael
    Ruzhansky, and Diana Stoeva, 5:425. Trends in Mathematics: Research Perspectives
    Ghent Analysis and PDE Cente. Birkhäuser Cham, 2024.'
  ieee: D. Brennecken and M. Rösler, “The Laplace transform in Dunkl theory,” in <i>Women
    in Analysis and PDE</i>, vol. 5, M. Chatzakou, M. Ruzhansky, and D. Stoeva, Eds.
    Birkhäuser Cham, 2024, p. 425.
  mla: Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl Theory.”
    <i>Women in Analysis and PDE</i>, edited by Marianna Chatzakou et al., vol. 5,
    Birkhäuser Cham, 2024, p. 425.
  short: 'D. Brennecken, M. Rösler, in: M. Chatzakou, M. Ruzhansky, D. Stoeva (Eds.),
    Women in Analysis and PDE, Birkhäuser Cham, 2024, p. 425.'
date_created: 2024-09-03T15:31:27Z
date_updated: 2024-09-05T06:58:54Z
department:
- _id: '555'
editor:
- first_name: Marianna
  full_name: Chatzakou, Marianna
  last_name: Chatzakou
- first_name: Michael
  full_name: Ruzhansky, Michael
  last_name: Ruzhansky
- first_name: Diana
  full_name: Stoeva, Diana
  last_name: Stoeva
intvolume: '         5'
language:
- iso: eng
page: '425'
publication: Women in Analysis and PDE
publication_identifier:
  isbn:
  - 978-3-031-57004-9
publication_status: published
publisher: Birkhäuser Cham
series_title: 'Trends in Mathematics: Research Perspectives Ghent Analysis and PDE
  Cente'
status: public
title: The Laplace transform in Dunkl theory
type: book_chapter
user_id: '82981'
volume: 5
year: '2024'
...
---
_id: '56366'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl
    convolution  of distributions , possibly both with non‐compact support, can be
    defined and study its analytic properties. We prove results on the (singular‐)support
    of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic
    regularity for a certain class of Dunkl operators, called elliptic Dunkl operators.
    Finally, for the root system  we consider the Riesz distributions  and prove that
    their Dunkl convolution exists and that  holds.</jats:p>
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
citation:
  ama: Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators.
    <i>Mathematische Nachrichten</i>. Published online 2024. doi:<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>
  apa: Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl
    operators. <i>Mathematische Nachrichten</i>. <a href="https://doi.org/10.1002/mana.202300370">https://doi.org/10.1002/mana.202300370</a>
  bibtex: '@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity
    for Dunkl operators}, DOI={<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>},
    journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik},
    year={2024} }'
  chicago: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl
    Operators.” <i>Mathematische Nachrichten</i>, 2024. <a href="https://doi.org/10.1002/mana.202300370">https://doi.org/10.1002/mana.202300370</a>.
  ieee: 'D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,”
    <i>Mathematische Nachrichten</i>, 2024, doi: <a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>.'
  mla: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.”
    <i>Mathematische Nachrichten</i>, Wiley, 2024, doi:<a href="https://doi.org/10.1002/mana.202300370">10.1002/mana.202300370</a>.
  short: D. Brennecken, Mathematische Nachrichten (2024).
date_created: 2024-10-07T11:44:00Z
date_updated: 2024-10-07T11:46:15Z
department:
- _id: '555'
doi: 10.1002/mana.202300370
language:
- iso: eng
publication: Mathematische Nachrichten
publication_identifier:
  issn:
  - 0025-584X
  - 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Dunkl convolution and elliptic regularity for Dunkl operators
type: journal_article
user_id: '55911'
year: '2024'
...
---
_id: '36294'
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
citation:
  ama: Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric
    series. <i>Transactions of the American Mathematical Society</i>. 2023;376(4):2419-2447.
    doi:<a href="https://doi.org/10.1090/tran/8860">10.1090/tran/8860</a>
  apa: Brennecken, D., &#38; Rösler, M. (2023). The Dunkl-Laplace transform and Macdonald’s
    hypergeometric series. <i>Transactions of the American Mathematical Society</i>,
    <i>376</i>(4), 2419–2447. <a href="https://doi.org/10.1090/tran/8860">https://doi.org/10.1090/tran/8860</a>
  bibtex: '@article{Brennecken_Rösler_2023, title={The Dunkl-Laplace transform and
    Macdonald’s hypergeometric series}, volume={376}, DOI={<a href="https://doi.org/10.1090/tran/8860">10.1090/tran/8860</a>},
    number={4}, journal={Transactions of the American Mathematical Society}, publisher={
    American Mathematical Society}, author={Brennecken, Dominik and Rösler, Margit},
    year={2023}, pages={2419–2447} }'
  chicago: 'Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and
    Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical
    Society</i> 376, no. 4 (2023): 2419–47. <a href="https://doi.org/10.1090/tran/8860">https://doi.org/10.1090/tran/8860</a>.'
  ieee: 'D. Brennecken and M. Rösler, “The Dunkl-Laplace transform and Macdonald’s
    hypergeometric series,” <i>Transactions of the American Mathematical Society</i>,
    vol. 376, no. 4, pp. 2419–2447, 2023, doi: <a href="https://doi.org/10.1090/tran/8860">10.1090/tran/8860</a>.'
  mla: Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s
    Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i>,
    vol. 376, no. 4,  American Mathematical Society, 2023, pp. 2419–47, doi:<a href="https://doi.org/10.1090/tran/8860">10.1090/tran/8860</a>.
  short: D. Brennecken, M. Rösler, Transactions of the American Mathematical Society
    376 (2023) 2419–2447.
date_created: 2023-01-12T08:32:44Z
date_updated: 2024-04-24T12:47:49Z
department:
- _id: '555'
doi: 10.1090/tran/8860
intvolume: '       376'
issue: '4'
language:
- iso: eng
page: 2419-2447
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: ' American Mathematical Society'
status: public
title: The Dunkl-Laplace transform and Macdonald’s hypergeometric series
type: journal_article
user_id: '37390'
volume: 376
year: '2023'
...
---
_id: '36271'
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
- first_name: Lorenzo
  full_name: Ciardo, Lorenzo
  last_name: Ciardo
citation:
  ama: Brennecken D, Hilgert J, Ciardo L. Algebraically Independent Generators for
    the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of
    Lie Theory</i>. 2021;31(2):459--468. doi:<a href="https://doi.org/10.48550/arXiv.2008.07479">10.48550/arXiv.2008.07479</a>
  apa: Brennecken, D., Hilgert, J., &#38; Ciardo, L. (2021). Algebraically Independent
    Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).
    <i>Journal of Lie Theory</i>, <i>31</i>(2), 459--468. <a href="https://doi.org/10.48550/arXiv.2008.07479">https://doi.org/10.48550/arXiv.2008.07479</a>
  bibtex: '@article{Brennecken_Hilgert_Ciardo_2021, title={Algebraically Independent
    Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)},
    volume={31}, DOI={<a href="https://doi.org/10.48550/arXiv.2008.07479">10.48550/arXiv.2008.07479</a>},
    number={2}, journal={Journal of Lie Theory}, publisher={Heldermann Verlag}, author={Brennecken,
    Dominik and Hilgert, Joachim and Ciardo, Lorenzo}, year={2021}, pages={459--468}
    }'
  chicago: 'Brennecken, Dominik, Joachim Hilgert, and Lorenzo Ciardo. “Algebraically
    Independent Generators for the Algebra of Invariant Differential Operators on
    SLn(R)/SOn(R).” <i>Journal of Lie Theory</i> 31, no. 2 (2021): 459--468. <a href="https://doi.org/10.48550/arXiv.2008.07479">https://doi.org/10.48550/arXiv.2008.07479</a>.'
  ieee: 'D. Brennecken, J. Hilgert, and L. Ciardo, “Algebraically Independent Generators
    for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R),” <i>Journal
    of Lie Theory</i>, vol. 31, no. 2, pp. 459--468, 2021, doi: <a href="https://doi.org/10.48550/arXiv.2008.07479">10.48550/arXiv.2008.07479</a>.'
  mla: Brennecken, Dominik, et al. “Algebraically Independent Generators for the Algebra
    of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i>,
    vol. 31, no. 2, Heldermann Verlag, 2021, pp. 459--468, doi:<a href="https://doi.org/10.48550/arXiv.2008.07479">10.48550/arXiv.2008.07479</a>.
  short: D. Brennecken, J. Hilgert, L. Ciardo, Journal of Lie Theory 31 (2021) 459--468.
date_created: 2023-01-12T08:23:28Z
date_updated: 2024-02-19T06:27:09Z
department:
- _id: '555'
- _id: '91'
doi: 10.48550/arXiv.2008.07479
intvolume: '        31'
issue: '2'
language:
- iso: eng
page: 459--468
publication: Journal of Lie Theory
publication_status: published
publisher: Heldermann Verlag
status: public
title: Algebraically Independent Generators for the Algebra of Invariant Differential
  Operators on SLn(R)/SOn(R)
type: journal_article
user_id: '49063'
volume: 31
year: '2021'
...