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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sampling expansions for functions having values in a Banach space


Authors: DeGuang Han and Ahmed I. Zayed
Journal: Proc. Amer. Math. Soc. 133 (2005), 3597-3607
MSC (2000): Primary 46B15, 46B45; Secondary 94A20, 42C40
Published electronically: June 8, 2005
MathSciNet review: 2163595
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Abstract: A sampling expansion for vector-valued functions having values in a Banach space, together with an inversion formula, is derived. The proof uses the concept of framing models of Banach spaces that generalizes the notion of frames in Hilbert spaces. Two examples illustrating the results are given, one involving functions having values in $L^{p}[-\pi, \pi], 1<p\leq 2$, and the second involving functions having values in $L^{p}(\mathbb{R} ) $ for $1 < p< \infty.$


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Additional Information

DeGuang Han
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: dhan@pegasus.cc.ucf.edu

Ahmed I. Zayed
Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
Email: azayed@math.depaul.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08163-3
PII: S 0002-9939(05)08163-3
Keywords: Framing models, Banach spaces, atomic decomposition, interpolation, the Whittaker-Shannon-Kotel'nikov sampling theorem, wavelet basis
Received by editor(s): November 21, 2003
Received by editor(s) in revised form: July 23, 2004
Published electronically: June 8, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society