Summation of Functions and Polynomial Solutions to a Multidimensional Difference Equation

We define a set of polynomial difference operators which allows us to solve the summation problem and describe the space of polynomial solutions for these operators in equations with the polynomial right-hand side. The criterion describing these polynomial difference operators was obtained. The theo...

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Bibliographic Details
Published inJournal of Siberian Federal University. Mathematics & Physics Vol. 26; no. 2; pp. 153 - 161
Main Authors Grigoriev, Andrey A, Leinartas, Evgeniy K, Lyapin, Alexander P
Format Journal Article
LanguageEnglish
Published Krasnoyarsk Siberian Federal University 01.04.2023
Subjects
Difference equations
Finite differences
Functions (mathematics)
Mathematical analysis
Mathematical functions
Operators (mathematics)
Polynomials
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Summary:We define a set of polynomial difference operators which allows us to solve the summation problem and describe the space of polynomial solutions for these operators in equations with the polynomial right-hand side. The criterion describing these polynomial difference operators was obtained. The theorem describing the space of polynomial solutions for the operators was proved.
ISSN:1997-1397
2313-6022