Stability of the convex Pompeiu sets
type: Item
instance of: scholarly article
title: Stability of the convex Pompeiu sets
zbMATH Open document ID: 0964.30001
DOI: 10.1007/BF01783689
author: Fausto Segala
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-07-09T00:00:00Z
review text: Let for some bounded set \(\Omega\) the function \(f=0\) be the only continuous function on the plane for which \[ \int_{\sigma(\Omega)} f(x) dx=0 \] for any rigid motion \(\sigma\) of the plane, then we say that a set \(\Omega \) is a Pompeiu set. The Pompeiu problem is to find all the bounded sets which are Pompeiu sets. The author proves that the Pompeiu convex domains are stable, i.e. if \(\Omega\) is a convex Pompeiu domain, then every convex domain close of \(\Omega \) is a Pompeiu set.
Mathematics Subject Classification ID: 30A99
zbMATH DE Number: 1471608
zbMATH Keywords: Pompeiu problem
zbMATH Keywords: stationary phase method
zbMATH Keywords: Pompeiu convex domains
reviewed by: Mykola Krasnoschok
MaRDI profile type: Publication
cites work: An inverse spectral theorem and its relation to the Pompeiu problem
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description: scientific article; zbMATH DE number 1471608