Advances in Difference Equations
Volume 2006 (2006), Article ID 51427, 10 pages

Difference equations on discrete polynomial hypergroups

Ágota Orosz

Institute of Mathematics and Informatics, University of Debrecen, Debrecen 4010, Hungary

Received 10 July 2005; Revised 24 October 2005; Accepted 30 October 2005

Copyright © 2006 Ágota Orosz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.