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Funktsional. Anal. i Prilozhen., 2010, Volume 44, Issue 3, Pages 50–62 (Mi faa2994)  

This article is cited in 8 scientific papers (total in 8 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.

DOI: https://doi.org/10.4213/faa2994

Full text: PDF file (231 kB)
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English version:
Functional Analysis and Its Applications, 2010, 44:3, 199–208

Bibliographic databases:

UDC: 517.98
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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Kreis, “Freimy i periodicheskie gruppy operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:2 (2012), 14–18  mathnet
    2. P. A. Terekhin, “Affinnye kvantovye freimy i ikh spektr”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:1(1) (2013), 32–36  mathnet
    3. Poumai Kh.T., Kaushik S.K., “Retro Banach Frames, Almost Exact Retro Banach Frames in Banach Spaces”, Bull. Math. Anal. Appl., 7:1 (2015), 38–48  mathscinet  isi
    4. Jahan Sh., Kumar V., Kaushik S.K., “On the Existence of Non-Linear Frames”, Arch. Math.-Brno, 53:2 (2017), 101–109  crossref  mathscinet  zmath  isi  scopus
    5. Poumai Kh.T., Kaushik S.K., “Some Results Concerning Riesz Bases and Frames in Banach Spaces”, Jordan J. Math. Stat., 10:1 (2017), 11–32  mathscinet  zmath  isi
    6. Speransky K.S., Terekhin P.A., “A Representing System Generated By the Szego Kernel For the Hardy Space”, Indag. Math.-New Ser., 29:5 (2018), 1318–1325  crossref  mathscinet  zmath  isi  scopus
    7. K. S. Speranskii, P. A. Terekhin, “O suschestvovanii freimov v prostranstve Khardi, postroennykh na osnove yadra Sege”, Izv. vuzov. Matem., 2019, no. 2, 57–68  mathnet  crossref
    8. Poumai Kh.T., Jahan Sh., “Atomic Systems For Operators”, Int. J. Wavelets Multiresolut. Inf. Process., 17:1 (2019), 1850066  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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