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Difference Equation for Functions Analytic Outside Two Squares

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Abstract

We consider a totality of two squares built on 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, which are analytic outside this set and vanish at infinity. The equation is applicable to the moments problem for entire functions of exponential type.

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Authors and Affiliations

  1. Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, Russia

    F. N. Garif’yanov

  2. Kazan National Research Technical University named after A. N. Tupolev, ul. K. Marksa 10, Kazan, 420111, Russia

    E. V. Strezhneva

Authors
  1. F. N. Garif’yanov
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  2. E. V. Strezhneva
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Corresponding author

Correspondence to F. N. Garif’yanov.

Additional information

Original Russian Text © F.N. Garif’yanov, E.V. Strezhneva, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 6, pp. 3–8.

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Garif’yanov, F.N., Strezhneva, E.V. Difference Equation for Functions Analytic Outside Two Squares. Russ Math. 62, 1–5 (2018). https://doi.org/10.3103/S1066369X18060014

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  • DOI: https://doi.org/10.3103/S1066369X18060014

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