Title

Sampling Expansions For Functions Having Values In A Banach Space

Keywords

Atomic decomposition; Banach spaces; Framing models; Interpolation; The Whittaker-Shannon-Kotel'nikov sampling theorem; Wavelet basis

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[-π, π], 1 < p ≤ 2, and the second involving functions having values in L P(ℝ) for 1 < p < ∞. ©2005 American Mathematical Society.

Publication Date

12-1-2005

Publication Title

Proceedings of the American Mathematical Society

Volume

133

Issue

12

Number of Pages

3597-3607

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-05-08163-3

Socpus ID

29144434468 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/29144434468

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