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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICS
On functions with the boundary Morera property in domains with piecewise-smooth boundary
A. M. Kytmanov, S. G. Myslivets Department of Mathematical Analysis and Differential Equations, Siberian Federal University, pr. Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
The problem of holomorphic extension of functions defined on the boundary of a domain into this domain is actual in multidimensional complex analysis. It has a long history, starting with the proceedings of Poincaré and Hartogs. This paper considers continuous functions defined on the boundary of a bounded domain $ D $ in $ \mathbb C ^ n $, $ n> 1 $, with piecewise-smooth boundary, and having the generalized boundary Morera property along the family of complex lines that intersect the boundary of a domain. Morera property is that the integral of a given function is equal to zero over the intersection of the boundary of the domain with the complex line. It is shown that such functions extend holomorphically to the domain $ D $. For functions of one complex variable, the Morera property obviously does not imply a holomorphic extension. Therefore, this problem should be considered only in the multidimensional case $ (n> 1) $. The main method for studying such functions is the method of multidimensional integral representations, in particular, the Bochner-Martinelli integral representation.
Keywords:
bounded domain with piecewise-smooth boundary, continuous function, Morera property, Bochner-Martinelli integral representation.
Received: 16.12.2020
Citation:
A. M. Kytmanov, S. G. Myslivets, “On functions with the boundary Morera property in domains with piecewise-smooth boundary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 50–58
Linking options:
https://www.mathnet.ru/eng/vuu754 https://www.mathnet.ru/eng/vuu/v31/i1/p50
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Abstract page: | 252 | Full-text PDF : | 132 | References: | 22 |
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