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Mat. Sb., 1997, Volume 188, Number 12, Pages 57–72 (Mi msb273)  

This article is cited in 12 scientific papers (total in 12 papers)

Coefficients with respect to orthogonal-like decomposition systems

T. P. Lukashenko

M. V. Lomonosov Moscow State University

Abstract: Properties of orthogonal-like decomposition systems are analyzed. It is shown in § 1 that such systems have most properties of orthogonal systems; the properties of the coefficients of the corresponding expansions are studied. A criterion enabling one to determine whether an orthogonal-like system is an orthogonal projection of an orthogonal system is established in § 2. In § 3 it is shown that Parseval's equality holds for a system satisfying certain natural conditions if and only if this is an orthogonal-like decomposition system.

DOI: https://doi.org/10.4213/sm273

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English version:
Sbornik: Mathematics, 1997, 188:12, 1783–1798

Bibliographic databases:

UDC: 517.518+517.982
MSC: 42C15
Received: 05.01.1997

Citation: T. P. Lukashenko, “Coefficients with respect to orthogonal-like decomposition systems”, Mat. Sb., 188:12 (1997), 57–72; Sb. Math., 188:12 (1997), 1783–1798

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. T. P. Lukashenko, “Properties of expansion systems similar to orthogonal ones”, Izv. Math., 62:5 (1998), 1035–1054  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Lukashenko, TP, “Generalized expansion systems similar to the orthogonal ones”, Vestnik Moskovskogo Universiteta Seriya 1 Matematika Mekhanika, 1998, no. 4, 6  mathscinet  zmath  isi
    3. T. P. Lukashenko, “On properties of generalized expansion systems that are similar to orthogonal systems”, Russian Math. (Iz. VUZ), 44:10 (2000), 30–44  mathnet  mathscinet  zmath  elib
    4. T. P. Lukashenko, “Analogs of the Kolmogorov–Seliverstov–Plessner theorem for nonorthogonal function systems”, Math. Notes, 67:1 (2000), 69–80  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. T. V. Rodionov, “Analogues of the Hausdorff–Young and Hardy–Littlewood theorems”, Izv. Math., 65:3 (2001), 589–606  mathnet  crossref  crossref  mathscinet  zmath
    6. B. S. Kashin, T. Yu. Kulikova, “A Note on the Description of Frames of General Form”, Math. Notes, 72:6 (2002), 863–867  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Napalkov, VV, “Various representations of the space of analytic functions and the problem of the dual space description”, Doklady Mathematics, 66:3 (2002), 335  mathscinet  zmath  isi  elib
    8. Napalkov, VV, “Integral transformations of Bergman weight spaces”, Doklady Mathematics, 70:1 (2004), 504  mathnet  mathscinet  zmath  isi  elib
    9. S. Ya. Novikov, “Bessel Sequences as Projections of Orthogonal Systems”, Math. Notes, 81:6 (2007), 800–809  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. A. A. Zakharova, “On the Properties of Generalized Frames”, Math. Notes, 83:2 (2008), 190–200  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. V. V. Napalkov (Jr.), “Orthosimilar expansion systems in space with reproducing kernel”, Ufa Math. J., 5:4 (2013), 88–100  mathnet  crossref  elib
    12. T. P. Lukashenko, “Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels”, Moscow University Mathematics Bulletin, 69:5 (2014), 211–216  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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