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Matematicheskie Zametki, 2008, Volume 83, Issue 2, Pages 210–220
DOI: https://doi.org/10.4213/mzm4417 (Mi mzm4417) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the Properties of Generalized Frames

A. A. Zakharova

M. V. Lomonosov Moscow State University
Full-text PDF (473 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm4417
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 AA with a bounded inverse acting from a separable space HH to L2(Ω)L2(Ω) (where ΩΩ is a space with countably additive measure) can be regarded as an operator assigning to each element x∈Hx∈H its coefficients in some generalized frame.
Keywords: frame, tight frame, integral frame, bounded operator, separable Hilbert space, Lebesgue space, countably additive measure.
Received: 30.05.2006
Revised: 21.03.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 2, Pages 190–200
DOI: https://doi.org/10.1134/S0001434608010215
Bibliographic databases:
UDC: 517.518+517.982
Language: Russian
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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    • This publication is cited in the following 4 articles:
    1. Jean Pierre ANTOINE, Giorgia BELLOMONTE, Camillo TRAPANI, “Weak AA-frames and weak AA-semi-frames”, Constructive Mathematical Analysis, 4:1 (2021), 104  crossref
    2. Syed Twareque Ali, Jean-Pierre Antoine, Jean-Pierre Gazeau, Theoretical and Mathematical Physics, Coherent States, Wavelets, and Their Generalizations, 2014, 37  crossref
    3. 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
    4. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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