Sampling in a Hilbert space
Author:
Ahmed I. Zayed
Journal:
Proc. Amer. Math. Soc. 124 (1996), 37673776
MSC (1991):
Primary 41A05, 41A35; Secondary 47A58
MathSciNet review:
1343731
Fulltext PDF Free Access
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Abstract: An analog of the WhittakerShannonKotel'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 boundaryvalue problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.
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Additional Information
Ahmed I. Zayed
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email:
fdzayed@ucf1vm.cc.ucf.edu
DOI:
http://dx.doi.org/10.1090/S0002993996035265
PII:
S 00029939(96)035265
Keywords:
Shannon's sampling theorem,
interpolation and approximation in a Hilbert space,
frames and frame operators
Received by editor(s):
May 30, 1994
Received by editor(s) in revised form:
June 5, 1995
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1996 American Mathematical Society
