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Izvestiya: Mathematics, 2012, Volume 76, Issue 4, Pages 688–701
DOI: https://doi.org/10.1070/IM2012v076n04ABEH002602 (Mi im7301) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the rate of convergence of orthorecursive expansions over non-orthogonal wavelets

A. Yu. Kudryavtsev

Moscow State Institute of International Relations (University) of the Ministry for Foreign Affairs of Russia
English version PDF (289 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n04ABEH002602
Abstract: We consider orthorecursive expansions (a generalization of orthogonal series) over families of non-orthogonal wavelets formed by the dyadic dilations and integer shifts of a given function $\varphi$. We estimate the rate of convergence of such expansions under some fairly relaxed restrictions on $\varphi$ and give examples of these estimates in some concrete cases.
Keywords: orthorecursive expansion, wavelets, Parseval's identity, greedy algorithm, rate of convergence, computational stability, Faber–Schauder system.
Received: 25.02.2011
Revised: 19.07.2011
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.982
MSC: 42C15, 46E20
Language: English
Original paper language: Russian
Citation: A. Yu. Kudryavtsev, “On the rate of convergence of orthorecursive expansions over non-orthogonal wavelets”, Izv. Math., 76:4 (2012), 688–701
Citation in format AMSBIB
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\paper On the rate of convergence of orthorecursive expansions over non-orthogonal wavelets
\jour Izv. Math.
\yr 2012
\vol 76
\issue 4
\pages 688--701
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  • https://doi.org/10.1070/IM2012v076n04ABEH002602
  • https://www.mathnet.ru/eng/im/v76/i4/p49
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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