Title

Sampling In A Hilbert Space

Keywords

Frames and frame operators; Interpolation and approximation in a Hilbert space; Shannon's sampling theorem

Abstract

An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hubert space. The proof uses the concept of frames and frame operators in a Hubert 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. ©1996 American Mathematical Society.

Publication Date

1-1-1996

Publication Title

Proceedings of the American Mathematical Society

Volume

124

Issue

12

Number of Pages

3767-3776

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/s0002-9939-96-03526-5

Socpus ID

21444458291 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/21444458291

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