A Wiener-Tauberian and a Pompeiu type theorems on the Laguerre hypergroup

DOI10.1016/j.jmaa.2008.10.023zbMath1157.43002OpenAlexW1976953694MaRDI QIDQ2518291

Belgacem Selmi, M. Mounir Nessibi

Publication date: 15 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.10.023

zbMATH Keywords

Fourier transformconvolutionRadon measureLaguerre hypergroupWiener-Tauberian theoremtranslation operatorsPompeiu-type theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis on hypergroups (43A62)

Related Items

Sufficient conditions for the weighted integrability of Fourier–Laguerre transforms, Bernstein's inequalities and Jackson's inverse theorems in the Laguerre hypergroup, Uncertainty inequalities on Laguerre hypergroup, A local central limit theorem on the Laguerre hypergroup

Cites Work

• The Pompeiu problem revisited
• Pompeiu's problem on symmetric spaces
• Spaces with an abstract convolution of measures
• Pompeiu's problem on spaces of constant curvature
• Injectivity of the Pompeiu transform in the Heisenberg group
• Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets
• Sobolev type spaces on the dual of the Laguerre hypergroup
• Spectral synthesis and the Pompeiu problem
• An algebra associated with the generalized sublaplacian
• Pompeiu-type theorem associated with the Dunkl operator on the real line
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