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This article is cited in 2 scientific papers (total in 2 papers)
On the Properties of Generalized Frames
A. A. Zakharova M. V. Lomonosov Moscow State University
Abstract:
In this paper, we introduce the notion of generalized frames and study their properties. Discrete and integral frames are special cases of generalized frames. We give criteria for generalized frames to be integral (discrete). We prove that any bounded operator $A$ with a bounded inverse acting from a separable space $H$ to $L_2(\Omega)$ (where $\Omega$ is a space with countably additive measure) can be regarded as an operator assigning to each element $x\in H$ its coefficients in some generalized frame.
Keywords:
frame, tight frame, integral frame, bounded operator, separable Hilbert space, Lebesgue space, countably additive measure
DOI:
https://doi.org/10.4213/mzm4417
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English version:
Mathematical Notes, 2008, 83:2, 190–200
Bibliographic databases:
UDC:
517.518+517.982 Received: 30.05.2006 Revised: 21.03.2007
Citation:
A. A. Zakharova, “On the Properties of Generalized Frames”, Mat. Zametki, 83:2 (2008), 210–220; Math. Notes, 83:2 (2008), 190–200
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz4417https://doi.org/10.4213/mzm4417 http://mi.mathnet.ru/eng/mz/v83/i2/p210
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This publication is cited in the following articles:
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Antoine J.-P., Balazs P., “Frames and semi-frames”, J. Phys. A, 44:20 (2011), 205201, 25 pp.
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Antoine J.-P., Balazs P., “Frames, semi-frames, and Hilbert scales”, Numer. Funct. Anal. Optim., 33:7-9 (2012), 736–769
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