Table of Contents
Journal of Operators
Volume 2015 (2015), Article ID 824549, 8 pages
http://dx.doi.org/10.1155/2015/824549
Research Article

On Ordinary, Linear -Difference Equations, with Applications to -Sato Theory

Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden

Received 24 September 2014; Revised 23 December 2014; Accepted 3 February 2015

Academic Editor: Claudio H. Morales

Copyright © 2015 Thomas Ernst. 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 purpose of this paper is to develop the theory of ordinary, linear -difference equations, in particular the homogeneous case; we show that there are many similarities to differential equations. In the second part we study the applications to a -analogue of Sato theory. The -Schur polynomials act as basis function, similar to -Appell polynomials. The Ward -addition plays a crucial role as operation for the function argument in the matrix -exponential and for the -Schur polynomials.