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
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.
difference equation, regularization method, doubly periodic group
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Siberian Mathematical Journal, 2003, 44:3, 435–442
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
\paper Difference equations for functions analytic beyond several squares
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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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
F. N. Garif'yanov, S. A. Modina, “The Carleman kernel and its applications”, Siberian Math. J., 53:6 (2012), 1011–1020
F. N. Garif'yanov, E. V. Strezhneva, “Difference equation for functions analytical outside two squares”, Russian Math. (Iz. VUZ), 62:6 (2018), 1–5
F. N. Garifyanov, “Summarnoe uravnenie dlya funktsii, golomorfnykh vne dvukh treugolnikov, i ego prilozheniya”, Izv. vuzov. Matem., 2019, no. 10, 21–27
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
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
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