Geodesic
On functions semi-analytical in the polydisk
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 3-7

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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. 
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A. I. Petrosyan; N. T. Gapoyan. On functions semi-analytical in the polydisk. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 3-7. http://geodesic.mathdoc.fr/item/UZERU_2009_2_a0/