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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 69–82
DOI: https://doi.org/10.4213/mzm5158 (Mi mzm5158) 		 
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
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DOI: https://doi.org/10.4213/mzm5158
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.
Received: 16.06.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 59–70
DOI: https://doi.org/10.1134/S0001434610010086
Bibliographic databases:
UDC: 517.444
Language: Russian
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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    • This publication is cited in the following 1 articles:
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