The Wigner and Weyl transforms attached to the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\)

DOI10.1007/s11868-021-00404-zzbMath1475.43005OpenAlexW3142006149MaRDI QIDQ2033467

Chirine Chettaoui, Amina Hassini, Khalifa Trimèche

Publication date: 17 June 2021

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-021-00404-z

zbMATH Keywords

Wigner transformWeyl transformCherednik Heckman-Opdam operatorsHeckman-Opdam-Jacobi theory

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Other functions coming from differential, difference and integral equations (33E30) Other transforms and operators of Fourier type (43A32) Hypergeometric functions associated with root systems (33C67)

Related Items (1)

Time–frequency analysis associated with the generalized Wigner transform

Cites Work

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• Singularities and analytic continuation of the Dunkl and the Jacobi-Cherednik intertwining operators and their duals
• Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC
• Weyl transforms
• Harmonic analysis for certain representations of graded Hecke algebras
• Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\)
• A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• The hypergeometric Wigner and Weyl transforms attached to the Cherednik operators in the W-invariant case
• The harmonic analysis associated to the Heckman-Opdam's theory and its application to a root system of type $BC_d$
• GENERALIZED WAVELETS AND THE GENERALIZED WAVELET TRANSFORM ON ℝ^dFOR THE HECKMAN-OPDAM THEORY
• THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEM OF TYPE $BC_2$

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