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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2009, Issue 2, Pages 3–7
(Mi uzeru254)
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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
On functions semi-analytical in the polydisk
A. I. Petrosyan, N. T. Gapoyan Chair of Matemathical Analysis YSU, Armenia
Abstract:
In the present paper the class of semi-analytical functions in the polydisk $ U^n\subset\mathbb{C}^n$ is introduced. This class is an extension of the set of holomorphic functions. For $ n =1$ the concept of semi-analyticity coincides with analyticity. The Dirichlet problem with values given on the distinguished boundary of the polydisk always has a solution in the set of real parts of semi-analytical functions. Therefore, to investigate semi-analytical functions one can apply the potential theory methods, like one does it for the one-dimensional case. In the present paper the Schwarz type integral representation for the above-mentioned functions is obtained.
Keywords:
polydisk, $n$-harmonic function, pluriharmonic function, the Schwarz formula.
Received: 24.02.2009 Accepted: 26.03.2009
Citation:
A. I. Petrosyan, N. T. Gapoyan, “On functions semi-analytical in the polydisk”, Proceedings of the YSU, Physical and Mathematical Sciences, 2009, no. 2, 3–7
Linking options:
https://www.mathnet.ru/eng/uzeru254 https://www.mathnet.ru/eng/uzeru/y2009/i2/p3
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Abstract page: | 85 | Full-text PDF : | 25 | References: | 17 |
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