Convergence of Classical Cardinal Series and Band Limited Special Functions

摘要

We consider the behavior of symmetric partial sums of the classical cardinal series. Necessary and sufficient conditions for convergence are recorded and a bound on the asymptotic behavior of the limiting function is established. Questions concerning sampling, uniqueness, and the effect of index shifts are also addressed. Examples of certain band limited special functions that can be expressed as limits of symmetric partial sums of classical cardinal series are included.