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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, Volume 31, Issue 1, Pages 50–58
DOI: https://doi.org/10.35634/vm210104
(Mi vuu754)
 

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
Full-text PDF (151 kB) Citations (2)
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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.
Funding agency Grant number
Russian Science Foundation 20-11-20117
The research is supported by grant of the Russian Science Foundation (project no. 20-11-20117).
Received: 16.12.2020
Bibliographic databases:
Document Type: Article
UDC: 517.55
MSC: 32A25, 32A40
Language: English
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
Citation in format AMSBIB
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\by A.~M.~Kytmanov, S.~G.~Myslivets
\paper On functions with the boundary Morera property in domains with piecewise-smooth boundary
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 1
\pages 50--58
\mathnet{http://mi.mathnet.ru/vuu754}
\crossref{https://doi.org/10.35634/vm210104}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000640022000004}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:24
     
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