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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 210–220 (Mi mz4417)  

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

Full text: PDF file (473 kB)
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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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Antoine J.-P., Balazs P., “Frames and semi-frames”, J. Phys. A, 44:20 (2011), 205201, 25 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Antoine J.-P., Balazs P., “Frames, semi-frames, and Hilbert scales”, Numer. Funct. Anal. Optim., 33:7-9 (2012), 736–769  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
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