Morera’s theorem and functional series in the class of $A$-analytic functions

Nasridin M. Jabborov

National University of Uzbekistan, Vuzgorodok, Tashkent, 100174, Uzbekistan

Abstract: The aim of this paper is to investigate $A$-analytic functions in a special case when the function $A$ is an anti-analytic function in a domain. We prove that a continuous function satisfying the integral condition of the Cauchy theorem is $A$-analytic (an analog of Morera's theorem, Sec. 2). In Sec. 3 we prove an analog of the Weierstrass theorem for functional series of $A$-analytic functions and the expansion of $A$-analytic functions into functional series (Sec. 4).

Keywords: $A$-analytic functions, analog of Morera's theorem, analog of the Weierstrass theorem, expansion of $A$-analytic functions.

UDC: 517.548.2

Received: 04.05.2017
Received in revised form: 18.10.2017
Accepted: 20.11.2017

Language: English

DOI: 10.17516/1997-1397-2018-11-1-50-59

Bibliographic databases:

•