@article{54820,
  abstract     = {{We study the asymptotic behaviour of Bessel functions associated of root
systems of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the
rank $n$ tends to infinity. In both cases, we characterize the possible limit
functions and the Vershik-Kerov type sequences of spectral parameters for which
such limits exist. In the type $A$ case, this gives a new and very natural
approach to recent results by Assiotis and Najnudel in the context of
$\beta$-ensembles in random matrix theory. These results generalize known facts
about the approximation of the (positive-definite) Olshanski spherical
functions of the space of infinite-dimensional Hermitian matrices over $\mathbb
F = \mathbb R, \mathbb C, \mathbb H$ (with the action of the associated
infinite unitary group) by spherical functions of finite-dimensional spaces of
Hermitian matrices. In the type B case, our results include asymptotic results
for the spherical functions associated with the Cartan motion groups of
non-compact Grassmannians as the rank goes to infinity, and a classification of
the Olshanski spherical functions of the associated inductive limits.}},
  author       = {{Brennecken, Dominik and Rösler, Margit}},
  journal      = {{Indagationes Mathematicae}},
  publisher    = {{Elsevier}},
  title        = {{{Limits of Bessel functions for root systems as the rank tends to  infinity}}},
  doi          = {{10.1016/j.indag.2024.05.004}},
  year         = {{2024}},
}

@article{53300,
  author       = {{Brennecken, Dominik}},
  issn         = {{0022-247X}},
  journal      = {{Journal of Mathematical Analysis and Applications}},
  keywords     = {{Applied Mathematics, Analysis}},
  number       = {{2}},
  publisher    = {{Elsevier BV}},
  title        = {{{Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}}},
  doi          = {{10.1016/j.jmaa.2024.128125}},
  volume       = {{535}},
  year         = {{2024}},
}

@inbook{56001,
  author       = {{Brennecken, Dominik and Rösler, Margit}},
  booktitle    = {{Women in Analysis and PDE}},
  editor       = {{Chatzakou, Marianna and Ruzhansky, Michael and Stoeva, Diana}},
  isbn         = {{978-3-031-57004-9}},
  pages        = {{425}},
  publisher    = {{Birkhäuser Cham}},
  title        = {{{The Laplace transform in Dunkl theory}}},
  volume       = {{5}},
  year         = {{2024}},
}

@article{56366,
  abstract     = {{<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       = {{Brennecken, Dominik}},
  issn         = {{0025-584X}},
  journal      = {{Mathematische Nachrichten}},
  publisher    = {{Wiley}},
  title        = {{{Dunkl convolution and elliptic regularity for Dunkl operators}}},
  doi          = {{10.1002/mana.202300370}},
  year         = {{2024}},
}

@article{36294,
  author       = {{Brennecken, Dominik and Rösler, Margit}},
  journal      = {{Transactions of the American Mathematical Society}},
  number       = {{4}},
  pages        = {{2419--2447}},
  publisher    = {{ American Mathematical Society}},
  title        = {{{The Dunkl-Laplace transform and Macdonald’s hypergeometric series}}},
  doi          = {{10.1090/tran/8860}},
  volume       = {{376}},
  year         = {{2023}},
}

@article{36271,
  author       = {{Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}},
  journal      = {{Journal of Lie Theory}},
  number       = {{2}},
  pages        = {{459----468}},
  publisher    = {{Heldermann Verlag}},
  title        = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}}},
  doi          = {{10.48550/arXiv.2008.07479}},
  volume       = {{31}},
  year         = {{2021}},
}