Characterization of the support for the hypergeometric Fourier transform of the \(W\)-invariant functions and distributions on \(\mathbb R ^d\) and Roe's theorem

DOI10.1186/1029-242X-2014-99zbMath1337.42006OpenAlexW2140408165WikidataQ59318295 ScholiaQ59318295MaRDI QIDQ261137

Khalifa Trimèche, Hatem Mejjaoli

Publication date: 22 March 2016

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

Full work available at URL: https://doi.org/10.1186/1029-242x-2014-99

zbMATH Keywords

generalized tempered distributionsCherednik operatorsHeckman-Opdam Laplacianhypergeometric Fourier transformreal Paley-Wiener theoremsRoe's theorem

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (13)

Paley-Wiener theorems for the two-sided quaternion Fourier transform ⋮ Paley-Wiener theorems of generalized Fourier transform associated with a Cherednik type operator on the real line ⋮ Spectral theorems associated with the Cherednik operators on \(\mathbb R^d\) ⋮ Boundedness and compactness of Heckman-Opdam two-wavelet multipliers ⋮ Characterization for the spectrum of the hypergeometric Fourier transform in terms of the generalized resolvent function ⋮ Properties of the fractional Clifford–Fourier transform ⋮ Wavelet packet analysis in the framework of Heckman-Opdam theory on \(\mathbb{R}^d \) ⋮ Localization operators associated with the hypergeometric Wigner transform related to the Cherednik operators in the case of the root system \(BC_d\) ⋮ Localization operators and scalogram associated with the generalized continuous wavelet transform on $\mathbb{R}^d$ for the Heckman–Opdam theory ⋮ SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS ⋮ QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM ⋮ Time–frequency analysis associated with the generalized Wigner transform ⋮ On the range of the Opdam-Cherednik transform and Roe's theorem in the Cherednik setting

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