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Sibirsk. Mat. Zh., 2003, Volume 44, Number 3, Pages 550–559 (Mi smj1197)  

This article is cited in 6 scientific papers (total in 6 papers)

Difference equations for functions analytic beyond several squares

F. N. Garif'yanov

Kazan State Power Engineering University

Abstract: We consider some set of squares constructed for the primitive periods 1 and $i$ and sufficiently distant from each other. In a neighborhood of this set we study a four-element difference equation with constant coefficients whose linear stifts are generators of the corresponding doubly periodic group and their inverses. A solution is sought in the class of functions analytic beyond this set and vanishing at infinity. We show that the solvability of the problem depends essentially not only on the choice of the coefficients but also on the disposition of the squares.

Keywords: difference equation, regularization method, doubly periodic group

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English version:
Siberian Mathematical Journal, 2003, 44:3, 435–442

Bibliographic databases:

UDC: 517.93
Received: 29.10.2002

Citation: F. N. Garif'yanov, “Difference equations for functions analytic beyond several squares”, Sibirsk. Mat. Zh., 44:3 (2003), 550–559; Siberian Math. J., 44:3 (2003), 435–442

Citation in format AMSBIB
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\by F.~N.~Garif'yanov
\paper Difference equations for functions analytic beyond several squares
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 3
\pages 550--559
\mathnet{http://mi.mathnet.ru/smj1197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1984703}
\zmath{https://zbmath.org/?q=an:1029.30023}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 3
\pages 435--442
\crossref{https://doi.org/10.1023/A:1023856613786}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. N. Garif'yanov, E. V. Nasyrova, “Regularization of linear difference equations with analytic coefficients and their applications”, Russian Math. (Iz. VUZ), 55:11 (2011), 66–70  mathnet  crossref  mathscinet
    2. F. N. Garif'yanov, S. A. Modina, “The Carleman kernel and its applications”, Siberian Math. J., 53:6 (2012), 1011–1020  mathnet  crossref  mathscinet  isi  elib  elib
    3. F. N. Garif'yanov, E. V. Strezhneva, “Difference equation for functions analytical outside two squares”, Russian Math. (Iz. VUZ), 62:6 (2018), 1–5  mathnet  crossref  isi
    4. F. N. Garifyanov, “Summarnoe uravnenie dlya funktsii, golomorfnykh vne dvukh treugolnikov, i ego prilozheniya”, Izv. vuzov. Matem., 2019, no. 10, 21–27  mathnet  crossref
    5. F. N. Garifyanov, E. V. Strezhneva, “O probleme momentov dlya tselykh funktsii na neskolkikh luchakh, indutsirovannoi kvadratom”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2019, 119–126  mathnet  crossref  elib
    6. Garif'yanov F.N., Strezhneva E.V., “on a Difference Equation Generated By Two “Close” Squares”, Lobachevskii J. Math., 40:1, SI (2019), 55–59  crossref  mathscinet  zmath  isi  scopus
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