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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 4, Pages 49–64 (Mi izv7301)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/im7301

Full text: PDF file (516 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:4, 688–701

Bibliographic databases:

UDC: 517.518+517.982
MSC: 42C15, 46E20
Received: 25.02.2011
Revised: 19.07.2011

Citation: A. Yu. Kudryavtsev, “On the rate of convergence of orthorecursive expansions over non-orthogonal wavelets”, Izv. RAN. Ser. Mat., 76:4 (2012), 49–64; Izv. Math., 76:4 (2012), 688–701

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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. Galatenko V.V. Lukashenko T.P. Sadovnichiy V.A., “Convergence Almost Everywhere of Orthorecursive Expansions in Functional Systems”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, ed. Sadovnichiy V. Zgurovsky M., Springer Int Publishing Ag, 2016, 3–11  crossref  mathscinet  zmath  isi  scopus
    2. I. S. Baranova, “Asymptotic properties of coefficients of orthorecursive expansions over indicators of dyadic intervals”, Moscow University Mathematics Bulletin, 74:5 (2019), 175–181  mathnet  crossref  mathscinet  isi
    3. V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “Ortorekursivnye razlozheniya i ikh svoistva”, Materialy Voronezhskoi zimneimatematicheskoi shkolySovremennye metody teorii funktsiii smezhnye problemy.28 yanvarya–2 fevralya 2019 g.Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 170, VINITI RAN, M., 2019, 62–70  mathnet  crossref
    4. Kalmynin A.B., Kosenko P.R., “Orthorecursive Expansion of Unity”, Int. J. Number Theory, 16:6 (2020), 1209–1226  crossref  mathscinet  isi
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