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Difference equations on discrete polynomial hypergroups

Abstract

The classical theory of homogeneous and inhomogeneous linear difference equations with constant coefficients on the set of integers or nonnegative integers provides effective solution methods for a wide class of problems arising from different fields of applications. However, linear difference equations with nonconstant coefficients present another important class of difference equations with much less highly developed methods and theories. In this work we present a new approach to this theory via polynomial hypergroups. It turns out that a major part of the classical theory can be converted into hypergroup language and technique, providing effective solution methods for a wide class of linear difference equations with nonconstant coefficients.

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Correspondence to Ágota Orosz.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Orosz, Á. Difference equations on discrete polynomial hypergroups. Adv Differ Equ 2006, 051427 (2006). https://doi.org/10.1155/ADE/2006/51427

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation