On sampling theory and basic Sturm–Liouville systems

We investigate the sampling theory associated with basic Sturm–Liouville 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 equa...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-09, Vol.206 (1), p.73-85
Main Authors: Annaby, M.H., Bustoz, J., Ismail, M.E.H.
Format: Article
Language:English
Subjects:
[formula omitted]-Sturm–Liouville problems
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Green's function
Integral transforms, operational calculus
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sampling theory
Sciences and techniques of general use
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Summary:We investigate the sampling theory associated with basic Sturm–Liouville 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 Sturm–Liouville systems. Examples involving basic sine and cosine transforms are given.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.05.024