Morera’s theorem and functional series in the class of $A$-analytic functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 50-59
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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.
@article{JSFU_2018_11_1_a7,
author = {Nasridin M. Jabborov},
title = {Morera{\textquoteright}s theorem and functional series in the class of $A$-analytic functions},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {50--59},
publisher = {mathdoc},
volume = {11},
number = {1},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a7/}
}
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%0 Journal Article %A Nasridin M. Jabborov %T Morera’s theorem and functional series in the class of $A$-analytic functions %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2018 %P 50-59 %V 11 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a7/ %G en %F JSFU_2018_11_1_a7
Nasridin M. Jabborov. Morera’s theorem and functional series in the class of $A$-analytic functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 50-59. http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a7/