Morera’s theorem and functional series in the class of $A$-analytic functions
Nasridin M. Jabborov
National University of Uzbekistan,
Vuzgorodok, Tashkent, 100174,
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).
$A$-analytic functions, analog of Morera's theorem, analog of the Weierstrass theorem, expansion of $A$-analytic functions.
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Received in revised form: 18.10.2017
Nasridin M. Jabborov, “Morera’s theorem and functional series in the class of $A$-analytic functions”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 50–59
Citation in format AMSBIB
\paper Morera’s theorem and functional series in the class of $A$-analytic functions
\jour J. Sib. Fed. Univ. Math. Phys.
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