Email this article On a Difference Equation Generated by Two “Close” Squares
- Authors: Garif’yanov F.N.1, Strezhneva E.V.2
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Affiliations:
- Kazan State Power Engineering University
- Kazan National Research Technical University named after A. N. Tupolev
- Issue: Vol 40, No 1 (2019)
- Pages: 55-59
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/203757
- DOI: https://doi.org/10.1134/S1995080219010074
- ID: 203757
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Abstract
We consider a set of two squares constructed for the primitive periods 1 and i and having four vertices on one straight line. In a neighborhood of this set, we study a four-element difference equation with constant coefficients. The linear shifts of this equation are the generating transformations of the corresponding doubly periodic group and their inverse transformations. The solution is sought in the class of functions that are analytic outside this set and vanish at infinity. We give some applications to the moment problem for entire functions of exponential type.
About the authors
F. N. Garif’yanov
Kazan State Power Engineering University
Author for correspondence.
Email: f.garifyanov@mail.ru
Russian Federation, Kazan
E. V. Strezhneva
Kazan National Research Technical University named after A. N. Tupolev
Author for correspondence.
Email: strezh@yandex.ru
Russian Federation, Kazan
