ON FUNCTIONS SEMI-ANALYTICAL IN THE POLYDISK

Authors

  • A. I. Petrosyan Chair of Matemathical Analysis, YSU, Armenia
  • N. T. Gapoyan Chair of Mathematical Analysis, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2009.43.2.003

Keywords:

polydisk, n-harmonic function, pluriharmonic function, Schwarz formula

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.

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Published

2009-06-26

How to Cite

Petrosyan, A. I., & Gapoyan, N. T. (2009). ON FUNCTIONS SEMI-ANALYTICAL IN THE POLYDISK. Proceedings of the YSU A: Physical and Mathematical Sciences, 43(2 (219), 3–7. https://doi.org/10.46991/PYSU:A/2009.43.2.003

Issue

Section

Mathematics