Sampling in a Hilbert space

Zayed, Ahmed

doi:10.1090/S0002-9939-96-03526-5

Sampling in a Hilbert space
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by Ahmed I. Zayed PDF

Proc. Amer. Math. Soc. 124 (1996), 3767-3776 Request permission

Abstract:

An analog of the Whittaker-Shannon-Kotel′nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.

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