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This article is cited in 18 scientific papers (total in 18 papers)
Frames in Banach Spaces
P. A. Terekhin Saratov State University named after N. G. Chernyshevsky
Abstract:
The notion of a frame in a Banach space with respect to a model space of sequences is introduced. This notion is different from the notions of an atomic decomposition, Banach frame in the sense of Gröchenig, (unconditional) Schauder frame in the sense of Han and Larson, and other known definitions of frames for Banach spaces. The frames introduced in this paper are shown to play a universal role in the solution of the general problem of representation of functions by series. A projective description of these frames is given. A criterion for the existence of a linear frame expansion algorithm and an analogue of the extremality property for a frame expansion are obtained.
Keywords:
frame, Banach frame, atomic decomposition, representation system, basis, projector, coefficient space, null series, complemented subspace.
Received: 15.04.2009
Citation:
P. A. Terekhin, “Frames in Banach Spaces”, Funktsional. Anal. i Prilozhen., 44:3 (2010), 50–62; Funct. Anal. Appl., 44:3 (2010), 199–208
Linking options:
https://www.mathnet.ru/eng/faa2994https://doi.org/10.4213/faa2994 https://www.mathnet.ru/eng/faa/v44/i3/p50
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Abstract page: | 964 | Full-text PDF : | 412 | References: | 113 | First page: | 32 |
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