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Matematicheskie Zametki, 2012, Volume 92, Issue 5, Pages 707–720
DOI: https://doi.org/10.4213/mzm8933
(Mi mzm8933)
 

This article is cited in 9 scientific papers (total in 9 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
Full-text PDF (566 kB) Citations (9)
References:
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 φφ. It is established that, under certain not too rigid constraints on the function φφ, the expansion for any function fL2(R) converges to f in L2(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.
Received: 14.09.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 5, Pages 643–656
DOI: https://doi.org/10.1134/S0001434612110077
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.982
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/mzm8933
  • https://doi.org/10.4213/mzm8933
  • https://www.mathnet.ru/eng/mzm/v92/i5/p707
  • This publication is cited in the following 9 articles:
    1. P. A. Terekhin, “Ortorekursivnye razlozheniya, porozhdennye yadrom Sege”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:4 (2023), 443–455  mathnet  crossref
    2. V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “Orthorecursive Expansions and Their Properties”, J Math Sci, 263:4 (2022), 522  crossref
    3. 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  mathscinet  zmath  adsnasa  isi  elib
    4. Filippov V.I., “Series With Integer Coefficients By Systems of Contractions and Shifts of One Function”, Lobachevskii J. Math., 41:11, SI (2020), 2143–2148  crossref  mathscinet  isi  scopus
    5. V. I. Filippov, “Series of Fourier type with integer coefficients by systems of dilates and translates of one function in Lp, p1”, Russian Math. (Iz. VUZ), 63:6 (2019), 51–57  mathnet  crossref  crossref  isi
    6. 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
    7. V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “Ortorekursivnye razlozheniya i ikh svoistva”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 170, VINITI RAN, M., 2019, 62–70  mathnet  crossref
    8. 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
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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