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About Functional Equation, Generated by Equilateral Triangle

Authors
  • Garifyanov, F. N.1
  • Strezhneva, E. V.2
  • 1 Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, Tatarstan, 420008, Russia , Kazan, Tatarstan (Russia)
  • 2 Kazan National Research Technical University, ul. K. Marksa 10, Kazan, Tatarstan, 420111, Russia , Kazan, Tatarstan (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Mar 21, 2018
Volume
39
Issue
2
Pages
204–208
Identifiers
DOI: 10.1134/S1995080218020129
Source
Springer Nature
Keywords
License
Yellow

Abstract

We considered 6-fold linear equation in the class of analytic functions outside the equilateral triangle and vanishing at infinity. We proposed a method of equivalent regularization, using the theory of boundary value problem of Carleman. Also, the paper is dedicated to applications to the problem of moments for entire functions of exponential type. In particular, we construct a system of functions biorthogonal whit piecewise-quasipolynomial weight to some power system on the three rays. The indicator of such functions is a piecewise-trigonometric function, with a period of 2π/3.

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