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Mat. Zametki, 2012, Volume 92, Issue 5, Pages 707–720 (Mi mz8933)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets

A. Yu. Kudryavtsev

Moscow State Institute of International Relations (University) of the Ministry for Foreign Affairs of Russia

Abstract: The present paper is concerned with orthorecursive expansions which are generalizations of orthogonal series to families of nonorthogonal wavelets, binary contractions and integer shifts of a given function $\varphi$. It is established that, under certain not too rigid constraints on the function $\varphi$, the expansion for any function $f\in L^2(\mathbb{R})$ converges to $f$ in $L^2(\mathbb{R})$. Such an expansion method is stable with respect to errors in the calculation of the coefficients. The results admit a generalization to the $n$-dimensional case.

Keywords: orthorecursive expansion, nonorthogonal wavelets, Parseval's equality, Bessel's identity, trigonometric system, Jackson's inequality

DOI: https://doi.org/10.4213/mzm8933

Full text: PDF file (566 kB)
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English version:
Mathematical Notes, 2012, 92:5, 643–656

Bibliographic databases:

UDC: 517.518+517.982
Received: 14.09.2011

Citation: A. Yu. Kudryavtsev, “On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets”, Mat. Zametki, 92:5 (2012), 707–720; Math. Notes, 92:5 (2012), 643–656

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. Kh. Kh. Kh. Al-Dzhourani, V. A. Mironov, P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Polnota i minimalnost”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:3 (2016), 247–256  mathnet  crossref  mathscinet  elib
    2. 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, eds. Sadovnichiy V., Zgurovsky M., Springer Int Publishing Ag, 2016, 3–11  crossref  mathscinet  zmath  isi  scopus
    3. V. I. Filippov, “Ryady tipa Fure s tselymi koeffitsientami po sistemam iz szhatii i sdvigov odnoi funktsii v prostranstvakh $L_p$, $p\geq 1$”, Izv. vuzov. Matem., 2019, no. 6, 58–64  mathnet  crossref
    4. 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
    5. 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
    6. V. I. Filippov, “Integer expansion in systems of translates and dilates of a single function”, Izv. Math., 84:4 (2020), 796–806  mathnet  crossref  crossref  isi
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