This article is cited in 16 papers

Extremal cases of the Pompeiu problem

V. V. Volchkov

Donetsk National University

Abstract: The Pompeiu problem is studied for functions defined on a ball $B\subset\mathbb R^n$ and having zero integrals over all sets congruent to a given compact set $K\subset B$. The problem of finding the least radius $r=r(K)$ of $B$ for which $K$ is a Pompeiu set is considered. The solution is obtained for the cases in which $K$ is a cube or a hemisphere.

UDC: 517

Received: 01.10.1993

DOI: 10.4213/mzm1761

 English version: Mathematical Notes, 1996, 59:5, 482–489

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