Morera’s Theorem and Functional Series in the Class of A-analytic Functions

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).