Hankel transform, \(\mathcal{K}\)-Bessel functions and zeta distributions in the Dunkl setting

DOI10.1016/j.jmaa.2024.128125arXiv2303.15952OpenAlexW4390843380MaRDI QIDQ6192939

Dominik Brennecken

Publication date: 12 March 2024

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.15952

zbMATH Keywords

Laplace transformHankel transformJack polynomialsDunkl theoryhypergeometric functions associated with root systemszeta distributions

Mathematics Subject Classification ID

Integral transforms of special functions (44A20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Hypergeometric functions associated with root systems (33C67)

Cites Work

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• A geometric quantization of the Kostant-Sekiguchi correspondence for scalar type unitary highest weight representations
• An extension problem for \(C^\infty\) functions with symmetries
• Bessel functions of matrix argument
• Fonctions de Bessel sur une algèbre de Jordan. (Bessel functions on a Jordan algebra)
• The Dunkl transform
• The Calogero-Sutherland model and generalized classical polynomials
• Zeta distributions associated to a representation of a Jordan algebra
• Some combinatorial properties of Jack symmetric functions
• The binomial formula for nonsymmetric Macdonald polynomials
• Nonsymmetric Jack polynomials and integral kernels
• Riesz distributions and Laplace transform in the Dunkl setting of type A
• Biorthogonal expansion of non-symmetric Jack functions
• Riesz potentials and integral geometry in the space of rectangular matrices
• Differentiable even functions
• Differential-Difference Operators Associated to Reflection Groups
• Extension theorem of Whitney type for S(Rd+) by use of the Kernel theorem
• Orthogonal Polynomials of Several Variables
• The Dunkl-Laplace transform and Macdonald’s hypergeometric series

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