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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 6, Pages 3–8 (Mi ivm9363)  

Difference equation for functions analytical outside two squares

F. N. Garif'yanova, E. V. Strezhnevab

a Kazan State Power Engineering University, 51 Krasnosel'skaya str., Kazan, 420066 Russia
b Kazan National Research Technical University named after A.N. Tupolev, 10 K. Marks str., Kazan, 420111 Russia

Abstract: We consider a totality of two squares constructed by primitive periods $1$ and $i$ and sufficiently close to each other. In a vicinity of this set we investigate four-element difference equation with constant coefficients, whose linear shifts are generating transforms of the corresponding doubly periodic group and the inverse transforms. We seek a solution in a class of functions analytical outside this set and vanishing at infinity. We indicate applications to the moments problem for entire functions of exponential type.

Keywords: difference equations, regularization method, moments problem.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:6, 1–5

Bibliographic databases:

Document Type: Article
UDC: 517.944
Received: 28.03.2017

Citation: F. N. Garif'yanov, E. V. Strezhneva, “Difference equation for functions analytical outside two squares”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 6, 3–8; Russian Math. (Iz. VUZ), 62:6 (2018), 1–5

Citation in format AMSBIB
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\by F.~N.~Garif'yanov, E.~V.~Strezhneva
\paper Difference equation for functions analytical outside two squares
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 6
\pages 3--8
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\jour Russian Math. (Iz. VUZ)
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\vol 62
\issue 6
\pages 1--5
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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