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Mat. Sb., 1998, Volume 189, Number 7, Pages 3–22 (Mi msb343)  

This article is cited in 6 scientific papers (total in 6 papers)

Extremal problems on Pompeiu sets

V. V. Volchkov

Donetsk National University

Abstract: The local Pompeiu problem and related questions about functions with vanishing integrals over parallelepipeds are studied. One of the central results of the paper is the solution of the problem about the ball of smallest radius in which parallelepipeds of fixed size have the Pompeiu property. Several results of interest for complex analysis and approximation theory are obtained as consequences.

DOI: https://doi.org/10.4213/sm343

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English version:
Sbornik: Mathematics, 1998, 189:7, 955–976

Bibliographic databases:

UDC: 517.5
MSC: Primary 26B15, 53C65; Secondary 30E20
Received: 27.08.1997

Citation: V. V. Volchkov, “Extremal problems on Pompeiu sets”, Mat. Sb., 189:7 (1998), 3–22; Sb. Math., 189:7 (1998), 955–976

Citation in format AMSBIB
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\paper Extremal problems on Pompeiu sets
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\yr 1998
\vol 189
\issue 7
\pages 3--22
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\transl
\jour Sb. Math.
\yr 1998
\vol 189
\issue 7
\pages 955--976
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Volchkov, VV, “On polyhedra with the local Pompeiu property”, Doklady Mathematics, 62:1 (2000), 69  mathscinet  zmath  isi
    3. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Volchkov, VV, “On functions with vanishing integrals over ellipsoids”, Doklady Mathematics, 63:1 (2001), 25  mathscinet  zmath  isi
    5. Siberian Math. J., 43:2 (2002), 215–222  mathnet  crossref  mathscinet  zmath  isi  scopus
    6. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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