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Ufa Mathematical Journal, 2020, Volume 12, Issue 2, Pages 21–27
DOI: https://doi.org/10.13108/2020-12-2-21
(Mi ufa511)
 

This article is cited in 2 scientific papers (total in 2 papers)

On moment problem for entire functions generated by doubly periodic group

F. N. Garif'yanova, E. V. Strezhnevab

a Kazan State Power Engineering University, Krasnosel'skaya str. 51, 420066, Kazan, Russia
b Kazan National Research Technical University named after A. N. Tupolev – KAI, Karl Marx str. 10, 420111, Kazan, Russia
References:
Abstract: We consider a lacunar problem for Stieltjes moments with an exponential weight. The solution is sought in the class of entire functions of exponential type, the indicator diagram of which is a some square. We construct nontrivial solutions of the corresponding homogeneous problem. This problem is reduced to the study of a linear total equation in the class of functions holomorphic outside four squares. At infinity, they have zero of a multiplicity at least three. Their boundary values satisfy the Hölder condition on any compact set containing no square vertices. At most logarithmic singularities are allowed at these vertices. The solution is sought in the form of an Cauchy type integral over the boundary of these squares with an unknown density. A method for regularizing the total equation is proposed. The condition of equivalence of this regularization is clarified. We find particular case when the obtained Fredholm equation of the second kind is solvable. In order to do this, we employ the principle of contracting mappings in a Banach space.
Keywords: regularization method, boundary value problems for elliptic functions, moments of entire functions of exponential type.
Received: 09.10.2019
Bibliographic databases:
Document Type: Article
UDC: 517.547
MSC: 30E05, 30E20, 30E25
Language: English
Original paper language: Russian
Citation: F. N. Garif'yanov, E. V. Strezhneva, “On moment problem for entire functions generated by doubly periodic group”, Ufa Math. J., 12:2 (2020), 21–27
Citation in format AMSBIB
\Bibitem{GarStr20}
\by F.~N.~Garif'yanov, E.~V.~Strezhneva
\paper On moment problem for entire functions generated by doubly periodic group
\jour Ufa Math. J.
\yr 2020
\vol 12
\issue 2
\pages 21--27
\mathnet{http://mi.mathnet.ru//eng/ufa511}
\crossref{https://doi.org/10.13108/2020-12-2-21}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000607969100003}
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  • https://www.mathnet.ru/eng/ufa511
  • https://doi.org/10.13108/2020-12-2-21
  • https://www.mathnet.ru/eng/ufa/v12/i2/p21
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:186
    Russian version PDF:54
    English version PDF:17
    References:30
     
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