The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem
type: Item
instance of: scholarly article
title: The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem
zbMATH Open document ID: 0876.43002
DOI: 10.1007/BF02761653
author: Rama Rawat
author: Alladi Sitaram
published in: Israel Journal of Mathematics
publication date: 1997-11-20T00:00:00Z
review text: \textit{D. Pompeiu} [Bull. Sci. Math. (2), 53, 328-332 (1929; JFM 55.0138.04)] a associé à toute fonction \(f\in L^1_{\text{loc}}(\mathbb{R}^n)\) et à tout ensemble borné \(E\) de mesure de Lebesgue positive, une fonction \(P_Ef\) définie sur le groupe des déplacements de l'espace affine par \(P_Ef(\sigma)= \int_{\sigma(E)}f\) et a posé le problème de l'injectivité de \(P_E\). Le principal résultat obtenu ici est l'injectivité de \(P_E\) sur \(L^p(\mathbb{R}^n)\) lorsque \(1\leq p\leq2n/(n-1)\).
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 820105
zbMATH Keywords: affine space
zbMATH Keywords: transformation group
zbMATH Keywords: Pompeiu transform
zbMATH Keywords: Wiener-Tauberian theorem
zbMATH Keywords: JFM 55.0138.04
Wikidata QID: Q122646728
reviewed by: Noël Leblanc
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02761653
OpenAlex ID: W1979725778
description: scientific article; zbMATH DE number 820105