Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\)

DOI10.1007/S40306-020-00395-XzbMath1484.42029OpenAlexW3120344899MaRDI QIDQ2048960

Fida Bahba

Publication date: 24 August 2021

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40306-020-00395-x

zbMATH Keywords

waveletsgeneralized wavelet transformHeckman-Opdam-Jacobi operator

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Other functions coming from differential, difference and integral equations (33E30) Other transforms and operators of Fourier type (43A32) Reflection groups, reflection geometries (51F15) Hypergeometric functions associated with root systems (33C67)

Related Items (1)

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

Cites Work

• On the range of the Opdam-Cherednik transform and Roe's theorem in the Cherednik setting
• Functional analysis, Sobolev spaces and partial differential equations
• La \(g\)-fonction de Littlewood-Paley associée à un opérateur différentiel singulier sur \((0,\infty)\). (The Littlewood-Paley's \(g\)-function associated with à singular différential opérator on \((0,\infty)\))
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Mehler integral transform associated with Jacobi functions with respect to the dual variable
• Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups
• Continuous and discrete Bessel wavelet transforms.
• Harmonic analysis for certain representations of graded Hecke algebras
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
• An Introduction to Dunkl Theory and Its Analytic Aspects
• The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
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