Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups

DOI10.1007/BF01332821zbMath0893.43001OpenAlexW2033198446MaRDI QIDQ1383736

Walter R. Bloom, Zengfu Xu

Publication date: 16 August 1998

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178801

zbMATH Keywords

Fourier transformtempered distributionsSchwartz functionsAbel transformChebli-Trimeche hypergroups

Mathematics Subject Classification ID

Harmonic analysis on hypergroups (43A62) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (22)

Distributional Chébli-Trimèche transforms ⋮ Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ ⋮ MAXIMAL FUNCTIONS ON CHÉBLI–TRIMÈCHE HYPERGROUPS ⋮ Harmonic analysis and integral transforms associated with a class of a system of partial differential operators ⋮ Harmonic analysis and Hartley transform associated with the generalized differential-difference operator ⋮ On real Paley--Wiener theorems for certain integral transforms. ⋮ Spectral theorems associated with the Jacobi-Cherednik operator ⋮ On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line ⋮ VECTOR-VALUED THEOREM FOR THE UNCENTRED MAXIMAL OPERATOR ON BESSEL–KINGMAN HYPERGROUPS ⋮ Convolution operators on Schwartz spaces for Chébli--Trimèche hypergroups ⋮ \(L^{p}\)-Fourier analysis for certain differential-reflection operators ⋮ Hypercyclic and chaotic convolution operators on Chébli-Trimèche hypergroups ⋮ Weyl-Bessel transforms ⋮ The Fourier Chébli-Trimèche transform on Boehmians ⋮ Generalized wavelet transform associated with the Heckman-Opdam-Jacobi theory on \(\mathbb{R}^{d+1}\) ⋮ POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$ ⋮ Huygen principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian ⋮ Chébli-Trimèche hypergroups and \(W\)-type spaces ⋮ Fourier algebra of a hypergroup. I ⋮ Variation diminishing convolution kernels associated with second-order differential operators ⋮ Harmonic analysis associated with the generalized differential-difference operator on the real line and quantitative uncertainty principles for its Hartley transform ⋮ Harmonic analysis associated with the modified Cherednik type operator and quantitative uncertainty principles for its Hartley transform

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• Heat ``polynomials for a singular differential operator on (0,\(\infty)\)
• Laws of large numbers for hypergroups on \({\mathbb{R}}_+\)
• One-dimensional hypergroups
• Harmonic analysis of probability measures on hypergroups
• Spaces with an abstract convolution of measures
• Sur un théorème de Paley-Wiener associe à la décomposition spectrale d'un opérateur de Sturm-Liouville sur \([0, \infty\)]
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• The Measure Algebra of a Locally Compact Hypergroup

This page was built for publication: Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups