On sampling theory and basic SturmLiouville systems
Abstract
We investigate the sampling theory associated with basic SturmLiouville eigenvalue problems. We derive two sampling theorems for integral transforms whose kernels are basic functions and the integral is of Jackson's type. The kernel in the first theorem is a solution of a basic difference equation and in the second one it is expressed in terms of basic Green's function of the basic SturmLiouville systems. Examples involving basic sine and cosine transforms are given.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 September 2007
 Bibcode:
 2007JCoAM.206...73A
 Keywords:

 qSturmLiouville problems;
 Green's function;
 Sampling theory