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Matematicheskie Zametki, 1996, Volume 59, Issue 5, Pages 671–680
DOI: https://doi.org/10.4213/mzm1761 (Mi mzm1761) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Extremal cases of the Pompeiu problem

V. V. Volchkov

Donetsk National University
Full-text PDF (198 kB) Citations (13)
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DOI: https://doi.org/10.4213/mzm1761
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.
Received: 01.10.1993
English version:
Mathematical Notes, 1996, Volume 59, Issue 5, Pages 482–489
DOI: https://doi.org/10.1007/BF02308814
Bibliographic databases:
UDC: 517
Language: Russian
Citation: V. V. Volchkov, “Extremal cases of the Pompeiu problem”, Mat. Zametki, 59:5 (1996), 671–680; Math. Notes, 59:5 (1996), 482–489
Citation in format AMSBIB
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\jour Math. Notes
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\pages 482--489
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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