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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Kibirev V. V.
SOME PROPERTIES OF ANALYTICAL FUNCTIONAL ELEMENT // BSU bulletin. Mathematics, Informatics. - 2019. №1. . - С. 22-30.
Title:
SOME PROPERTIES OF ANALYTICAL FUNCTIONAL ELEMENT
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-1-22-30UDK: 517.55
Annotation:
The article introduces the concept of analytic functional element and the analyticity of function in n-dimensional point for functions of many complex variables. Fur- ther, we describe some properties of the theory of many complex variables and con- sider their application in the theory of differential equations. While using the Cauchy’s integral formula, various statements and implications from them are in- troduced, as well as for the functions of one complex variable. The uniformly con- vergent series of analytic functions are used for the proof of some theorems.
Keywords:
analytic functional element; analytic function; polycylindric domain; polycylinder; Cauchy’s integral formula; convergence of series; analytic continua- tion, modulus of analytic functional element; elementary neighborhood of point; boundary point distance.
List of references:
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Privalov I. I. Subgarmonicheskie funktsii [Subharmonic Functions]. Moscow; Leningrad, 1937. 200 p.

Fuks B. A. Vvedenie v teoriyu analiticheskikh funktsii mnogikh kompleksnykh peremennykh [Introduction to the Theory of Analytic Functions of Many Complex Va- riables]. Moscow: Nauka Publ., 1962. 420 p.

Shabat B. V. Vvedenie v kompleksnyi analiz [Introduction to Complex Analysis]. Moscow: Nauka Publ., 1976. 400 p.

Yanushauskas A. I. Analiticheskie i garmonicheskie funktsii mnogikh peremennykh [Analytic and Harmonic Functions of Many Variables]. Novosibirsk: Nauka Publ., 1981. 183 p.