Title:
Perturbations of Banach Frames and Atomic Decompositions
Perturbations of Banach Frames and Atomic Decompositions
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Author(s)
Christensen, Ole
Heil, Christopher E.
Heil, Christopher E.
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Abstract
Banach frames and atomic decompositions are sequences which have basis-like properties
but which need not be bases. In particular, they allow elements of a Banach space to be written as combinations of the frame or atomic decomposition elements in a stable manner. However, these representations
need not be unique. Such exibility is important in many applications. In this paper, we prove that
frames and atomic decompositions in Banach spaces are stable under small perturbations. Our results are
strongly related to classic results on perturbations of Paley/Wiener and Kato. We also consider duality
properties for atomic decompositions, and discuss the consequences for Hilbert frames.
Sponsor
National Science Foundation Grant DMS-9401340 and the MITRE Sponsored Research Program
Date Issued
1994-06
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Pre-print