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Izvestiya: Mathematics, 2011, Volume 75, Issue 2, Pages 413–443
DOI: https://doi.org/10.1070/IM2011v075n02ABEH002539
(Mi im4203)
 

This article is cited in 7 scientific papers (total in 7 papers)

Bases of exponentials, sines and cosines in weighted spaces on a finite interval

S. S. Pukhov

M. V. Lomonosov Moscow State University
References:
Abstract: We obtain a result concerning the basis property in a weighted space on an interval (a,a) for a system of exponentials generated by the zeros of the Fourier transform of a function with singularities at the ends of the support interval (a,a). For an arbitrary ΔC we find a criterion for the basis property of the system (ei(n+Δsignn)t)nZ in a weighted space on the interval (π,π) and the systems of sines (sin((n+Δ)t))nN and cosines 1(cos((n+Δ)t))nN in a weighted space on the interval (0,π). The weight is everywhere a finite product of polynomial functions.
Keywords: bases of exponentials, weighted spaces.
Received: 21.08.2009
Bibliographic databases:
Document Type: Article
UDC: 517.982.254
MSC: Primary 30B50; Secondary 42A05, 42A10, 42A63, 42C30
Language: English
Original paper language: Russian
Citation: S. S. Pukhov, “Bases of exponentials, sines and cosines in weighted spaces on a finite interval”, Izv. Math., 75:2 (2011), 413–443
Citation in format AMSBIB
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\by S.~S.~Pukhov
\paper Bases of exponentials, sines and cosines in weighted spaces on a~finite interval
\jour Izv. Math.
\yr 2011
\vol 75
\issue 2
\pages 413--443
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\crossref{https://doi.org/10.1070/IM2011v075n02ABEH002539}
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Linking options:
  • https://www.mathnet.ru/eng/im4203
  • https://doi.org/10.1070/IM2011v075n02ABEH002539
  • https://www.mathnet.ru/eng/im/v75/i2/p195
  • This publication is cited in the following 7 articles:
    1. M. I. Ismailov, I. F. Aliyarova, “On the basis property of the system of exponentials and trigonometric systems of sine and cosine functions in weighted grand Lebesgue spaces”, Moscow University Mathematics Bulletin, 79:2 (2024), 85–97  mathnet  crossref  crossref  elib
    2. Yu. A. Kriksin, V. F. Tishkin, “On an approximation by band-limited functions”, Dokl. Math., 110:3 (2024), 500–505  mathnet  mathnet  crossref  crossref
    3. Gasymov T.B., Akhtyamov A.M., Ahmedzade N.R., “On the Basicity of Eigenfunctions of a Second-Order Differential Operator With a Discontinuity Point in Weighted Lebesgue Spaces”, Proc. Inst. Math. Mech., 46:1 (2020), 32–44  crossref  mathscinet  isi  scopus
    4. V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for Lp-functionals”, Izv. Math., 82:2 (2018), 377–406  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Shukurov A.Sh., “On Basicity of the Degenerate Trigonometric System With Excess”, Acta Comment. Univ. Tartu. Math., 21:2 (2017), 249–257  crossref  mathscinet  zmath  isi  scopus
    6. S. S. Pukhov, “Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier–Stieltjes Transform”, Math. Notes, 95:6 (2014), 820–832  mathnet  crossref  crossref  mathscinet  isi  elib
    7. V. R. Fatalov, “Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for Lp-functionals, 0<p<”, Problems Inform. Transmission, 50:4 (2014), 371–389  mathnet  crossref  isi
    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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    Abstract page:794
    Russian version PDF:691
    English version PDF:23
    References:111
    First page:34
     
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