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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 3, Pages 550–559
(Mi smj1197)
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This article is cited in 7 scientific papers (total in 7 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.
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
Linking options:
https://www.mathnet.ru/eng/smj1197 https://www.mathnet.ru/eng/smj/v44/i3/p550
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