Sonine Formulas and Intertwining Operators in Dunkl Theory

DOI10.1093/imrn/rnz313OpenAlexW3098083448MaRDI QIDQ5066820

Michael Voit, Margit Rösler

Publication date: 30 March 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.02821

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items

Riesz distributions and Laplace transform in the Dunkl setting of type A

Cites Work

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• Angular momenta of relative equilibrium motions and real moment map geometry
• The wave equation for Dunkl operators
• A new integral formula for Heckman-Opdam hypergeometric functions
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• Invariant generalized functions in homogeneous domains
• The Dunkl transform
• The Calogero-Sutherland model and generalized classical polynomials
• The Selberg-Jack symmetric functions
• Orthogonal polynomials associated with root systems
• A Laplace-type representation of the generalized spherical functions associated with the root systems of type \(A\)
• Some combinatorial properties of Jack symmetric functions
• An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials
• Harmonic analysis for certain representations of graded Hecke algebras
• Positivity of Dunkl's intertwining operator
• Riesz distributions and Laplace transform in the Dunkl setting of type A
• Convolution algebras for Heckman-Opdam polynomials derived from compact Grassmannians
• Limit transition between hypergeometric functions of type BC and type A
• When is a Riesz distribution a complex measure?
• Certain Hypergeometric Series Related to the Root System BC
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• The importance of the Selberg integral
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Singular Polynomials for Finite Reflection Groups
• A Laplace-type representation for some generalized spherical functions of type $BC$
• Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones
• Paley–Wiener theorems for the Dunkl transform
• Orthogonal Polynomials of Several Variables