Advances in Difference Equations
Volume 2006 (2006), Article ID 51427, 10 pages
doi:10.1155/ADE/2006/51427
Difference equations on discrete polynomial hypergroups
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.
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.