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Mat. Zametki, 2010, Volume 87, Issue 1, Pages 69–82 (Mi mz5158)  

This article is cited in 1 scientific paper (total in 1 paper)

Sets with the Pompeiu Property on the Plane and on the Sphere

V. V. Volchkov, Vit.V.Volchkov

Donetsk National University

Abstract: We obtain new sufficient conditions under which a set on the plane has the Pompeiu property. This result allows us to construct first examples of domains with the Pompeiu property with non-Lipschitz (and even fractal) boundary. In addition, we study the problem of determining the least radius of the ball on the sphere in which a given set is a Pompeiu set. We obtain the solution of this problem in the case of a biangle and a spherical half-disk. We also consider some applications to questions of complex analysis.

Keywords: Pompeiu problem, Pompeiu property, non-Lipschitz boundary, biangle, spherical half-disk, Koch snowflake, Morera-type theorems, Laplace operator

DOI: https://doi.org/10.4213/mzm5158

Full text: PDF file (529 kB)
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English version:
Mathematical Notes, 2010, 87:1, 59–70

Bibliographic databases:

UDC: 517.444
Received: 16.06.2008

Citation: V. V. Volchkov, Vit.V.Volchkov, “Sets with the Pompeiu Property on the Plane and on the Sphere”, Mat. Zametki, 87:1 (2010), 69–82; Math. Notes, 87:1 (2010), 59–70

Citation in format AMSBIB
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\yr 2010
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\pages 69--82
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  • https://doi.org/10.4213/mzm5158
  • http://mi.mathnet.ru/eng/mz/v87/i1/p69

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ochakovskaya O.A., “The Pompeiu Property and Approximation in l-P By Linear Combinations of Shifts”, Dokl. Math., 89:2 (2014), 173–175  crossref  mathscinet  zmath  isi  scopus
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