Morera’s Theorem and Functional Series in the Class of A-analytic Functions
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https://elib.sfu-kras.ru/handle/2311/68745Author:
Jabborov, Nasridin M.
Жабборов, Насридин М.
Date:
2018-02Journal Name:
Журнал Сибирского федерального университета. Математика и физика. Journal of Siberian Federal University. Mathematics & Physics;2018 11 (1)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) Цель данной статьи — исследование A-аналитических функций в частном случае, когда функция A является антианалитической функцией в области. Доказано, что непрерывная функция,
удовлетворяющая интегральным условиям теоремы Коши, аналитическая (аналог теоремы Морера, sec. 2). В sec. 3 доказывается аналог теоремы Вейерштрасса для функционального ряда по A-аналитическим функциям и разложение A-аналитических функций в функциональные ряды (sec. 4)
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