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Sbornik: Mathematics, 1998, Volume 189, Issue 7, Pages 955–976
DOI: https://doi.org/10.1070/sm1998v189n07ABEH000343 (Mi sm343) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Extremal problems on Pompeiu sets

V. V. Volchkov

Donetsk National University
English version PDF (312 kB) Citations (6) Russian version article
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DOI: https://doi.org/10.1070/sm1998v189n07ABEH000343
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.
Received: 27.08.1997
Bibliographic databases:
UDC: 517.5
MSC: Primary 26B15, 53C65; Secondary 30E20
Language: English
Original paper language: Russian
Citation: V. V. Volchkov, “Extremal problems on Pompeiu sets”, Sb. Math., 189:7 (1998), 955–976
Citation in format AMSBIB
\Bibitem{Vol98}
\by V.~V.~Volchkov
\paper Extremal problems on Pompeiu sets
\jour Sb. Math.
\yr 1998
\vol 189
\issue 7
\pages 955--976
\mathnet{http://mi.mathnet.ru/eng/sm343}
\crossref{https://doi.org/10.1070/sm1998v189n07ABEH000343}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1659827}
\zmath{https://zbmath.org/?q=an:0957.53042}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000077042100001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0032220874}
Linking options:
  • https://www.mathnet.ru/eng/sm343
  • https://doi.org/10.1070/sm1998v189n07ABEH000343
  • https://www.mathnet.ru/eng/sm/v189/i7/p3
    Cycle of papers
    This publication is cited in the following 6 articles:
    1. V. V. Volchkov, “Local two-radii theorem in symmetric spaces”, Sb. Math., 198:11 (2007), 1553–1577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Siberian Math. J., 43:2 (2002), 215–222  mathnet  crossref  mathscinet  zmath  isi  scopus
    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. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Volchkov, VV, “On polyhedra with the local Pompeiu property”, Doklady Mathematics, 62:1 (2000), 69  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:750
    Russian version PDF:294
    English version PDF:55
    References:56
    First page:1
     
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