The Kramer Sampling Theorem Revisited
The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space \(\mathcal {H}\) through an \(\mathcal {H}\)-valued kernel K defined on an appropriate domain.
sampling formulas kramer kernels reproducing kernel hilbert spaces lagrange-type interpolation series zero-removing property semi-inner products reproducing kernel banach spaces reproducing distributions 46e22 42c15 94a20