Injectivity of the Pompeiu transform in the Heisenberg group

DOI10.1007/BF03008422zbMath0808.43002WikidataQ122750013 ScholiaQ122750013MaRDI QIDQ1326644

Daniel Pascuas, Mark L. Agranovsky, Der-Chen E. Chang, Carlos. A. Berenstein

Publication date: 12 March 1995

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

spherical functionsHeisenberg groupconvolution operatorGelfand transformlocally compact spacePompeiu problemWiener Tauberian theorems

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Harmonic analysis and spherical functions (43A90)

Related Items

Deconvolution for the Pompeiu Problem on the Heisenberg Group, I ⋮ The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem ⋮ Mean periodic functions on phase space and the Pompeiu problem with a twist ⋮ A theorem of the Wiener-Tauberian type for \(L^ 1(H^ n)\) ⋮ A local two radii theorem on the Chébli-Trimèche hypergroup ⋮ Pompeiu problem on product of Heisenberg groups ⋮ In memoriam: Lawrence Allen Zalcman (1943--2022) ⋮ Moment versions of the Morera problem in \(\mathbb C^n\) and \(\mathbb H^n\). ⋮ The pompeiu problem ⋮ Injectivity sets for spherical means on the Heisenberg group ⋮ On the injectivity of twisted spherical means of \(\mathbb{C}^n\) ⋮ Pompeiu-type theorem associated with the Dunkl operator on the real line ⋮ Injectivity sets for spherical means on the Heisenberg group ⋮ A Wiener-Tauberian and a Pompeiu type theorems on the Laguerre hypergroup ⋮ Gelfand pairs, \(K\)-spherical means and injectivity on the Heisenberg group ⋮ Hecke-Bochner identity and eigenfunctions associated to Gelfand pairs on the Heisenberg group

Cites Work

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• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group

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