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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 1, Pages 50–59 (Mi jsfu592)  

Moreras 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.

DOI: https://doi.org/10.17516/1997-1397-2018-11-1-50-59

Full text: PDF file (124 kB)
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Bibliographic databases:

UDC: 517.548.2
Received: 04.05.2017
Received in revised form: 18.10.2017
Accepted: 20.11.2017
Language:

Citation: Nasridin M. Jabborov, “Moreras 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
\Bibitem{Zha18}
\by Nasridin~M.~Jabborov
\paper Moreras theorem and functional series in the class of $A$-analytic functions
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 1
\pages 50--59
\mathnet{http://mi.mathnet.ru/jsfu592}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-1-50-59}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000431379500008}


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