Sampling expansions for functions having values in a Banach space
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- by DeGuang Han and Ahmed I. Zayed PDF
- Proc. Amer. Math. Soc. 133 (2005), 3597-3607 Request permission
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 $1 < p< \infty .$References
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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
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3597-3607
- MSC (2000): Primary 46B15, 46B45; Secondary 94A20, 42C40
- DOI: https://doi.org/10.1090/S0002-9939-05-08163-3
- MathSciNet review: 2163595