On one extremal problem of Pompeiu sets
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We determine upper bounds for the least radius of a ball in which a given set is a Pompeiu set (the set considered is a half right circular cone). The obtained estimates significantly improve known results.
KeywordsExtremal Problem Integral Geometry Close Location Circular Cone Half Cone
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- 1.L. Zalcman, “A bibliographic survey of Pompeiu problem,” in: B. Fuglede, M. Goldstein, W. Haussmann, et al. (editors), Approximation by Solutions of Partial Differential Equations, Springer (1992), pp. 185–194.Google Scholar
- 5.V. V. Volchkov and Vit. V. Volchkov, Geometric Aspects of the Mean Periodicity, Donetsk National University, Donetsk (2007).Google Scholar
- 9.P. A. Masharov, “Extremal problems of sets with local Pompeiu property,” Dopov. Nats. Akad. Nauk Ukr., No. 7, 25–29 (2001).Google Scholar
- 10.P. A. Masharov, “Solution of a local version of the Pompeiu problem for the Reuleaux triangle,” Visn. Dnipropetrovs’k. Univ., Ser. Mat., Issue 6, 72–81 (2001).Google Scholar
- 11.P. A. Masharov, “On cylinders with local Pompeiu property,” Visn. Donets’k. Nats. Univ., Ser. A, Pryrod. Nauky, No. 1, 21–25 (2000).Google Scholar