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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
References:
Abstract: The Pompeiu problem is studied for functions defined on a ball BRn and having zero integrals over all sets congruent to a given compact set KB. 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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\by V.~V.~Volchkov
\paper Extremal cases of the Pompeiu problem
\jour Mat. Zametki
\yr 1996
\vol 59
\issue 5
\pages 671--680
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\crossref{https://doi.org/10.4213/mzm1761}
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\zmath{https://zbmath.org/?q=an:1056.26501}
\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 5
\pages 482--489
\crossref{https://doi.org/10.1007/BF02308814}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996VM73200003}
Linking options:
  • https://www.mathnet.ru/eng/mzm1761
  • https://doi.org/10.4213/mzm1761
  • https://www.mathnet.ru/eng/mzm/v59/i5/p671
  • This publication is cited in the following 13 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. V. V. Volchkov, “Uniqueness theorems for solutions of the convolution equation on symmetric spaces”, Izv. Math., 70:6 (2006), 1077–1092  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Vit. V. Volchkov, “Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space”, Math. Notes, 74:1 (2003), 30–37  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Volchkov, VV, “Final version of the local two-radius theorem on the quaternion hyperbolic space”, Doklady Mathematics, 65:3 (2002), 389  mathscinet  zmath  isi
    5. V. V. Volchkov, “A definitive version of the local two-radii theorem on hyperbolic spaces”, Izv. Math., 65:2 (2001), 207–229  mathnet  crossref  crossref  mathscinet  zmath
    6. V. V. Volchkov, “Theorems on ball mean values in symmetric spaces”, Sb. Math., 192:9 (2001), 1275–1296  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Volchkov, VV, “On functions with vanishing integrals over ellipsoids”, Doklady Mathematics, 63:1 (2001), 25  mathscinet  zmath  isi
    8. V. V. Volchkov, “Extremal problems on Pompeiu sets. II”, Sb. Math., 191:5 (2000), 619–632  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Vit. V. Volchkov, “On functions with zero spherical means of complex hyperbolic spaces”, Math. Notes, 68:4 (2000), 436–443  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Volchkov, VV, “On polyhedra with the local Pompeiu property”, Doklady Mathematics, 62:1 (2000), 69  mathscinet  zmath  isi
    11. V. V. Volchkov, “Injectivity sets of the Pompeiu transform”, Sb. Math., 190:11 (1999), 1607–1622  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Volchkov, VV, “Functions with zero integrals over parallelepipeds”, Doklady Akademii Nauk, 369:4 (1999), 444  mathnet  mathscinet  zmath  isi
    13. V. V. Volchkov, “Extremal problems on Pompeiu sets”, Sb. Math., 189:7 (1998), 955–976  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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