On the injectivity of the Pompeiu transform for integral ball means
type: Item
instance of: scholarly article
title: On the injectivity of the Pompeiu transform for integral ball means
zbMATH Open document ID: 1243.44004
published in: Ukrainian Mathematical Journal
publication date: 2012-03-19T00:00:00Z
review text: The Pompeiu transform \(f\to P_rf\) is defined as a mapping from \(L^1_{\text{loc}}(\mathbb{R}^n)\) by the formula \[ P_r f(x)= \int_{|y|\leq r} f(x+ y)\,dy. \] In this paper the author deals with the problem of infectivity of this transform. The main result describes conditions under which the equation \(P_r f(x)= 0\) for all \(x\in\mathbb{R}^n\) leads to \(f=0\).
reviewed by: Khristo N. Boyadzhiev
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 6015823
zbMATH Keywords: Pompeiu transform
zbMATH Keywords: injectivity integral geometry
Wikidata QID: Q123075088
author: O. A. Ochakovskaya
MaRDI profile type: Publication
full work available at URL: s11253-011-0512-1
OpenAlex ID: W2020538102
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DOI: 10.1007/S11253-011-0512-1
description: scientific article; zbMATH DE number 6015823