Difference Equation for Functions Analytic Outside Two Squares

Difference Equation for Functions Analytic Outside Two Squares 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Mathematics Springer Journals

Difference Equation for Functions Analytic Outside Two Squares

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Publisher
Pleiades Publishing
Copyright
Copyright © 2018 by Allerton Press, Inc.
Subject
Mathematics; Mathematics, general
ISSN
1066-369X
eISSN
1934-810X
D.O.I.
10.3103/S1066369X18060014
Publisher site
See Article on Publisher Site

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.

Journal

Russian MathematicsSpringer Journals

Published: May 30, 2018

References

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