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Izvestiya: Mathematics, 2000, Volume 64, Issue 3, Pages 583–600
DOI: https://doi.org/10.1070/im2000v064n03ABEH000292
(Mi im292)
 

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

On the summability and convergence of non-harmonic Fourier series

A. M. Sedletskii
References:
Abstract: We consider systems of exponentials that are orthogonal to measures $d\sigma$ of a special form on $(-a,a)$. Under certain conditions on the summation method, these systems form summation bases $L^p(-a,a)$ and in $C_0$ (the subspace of $C[-a,a]$ orthogonal to $d\sigma$). With respect to these systems, Lipschitzian functions in $C_0$ are expanded into non-harmonic Fourier series that converge uniformly on $[-a,a]$.
Received: 03.11.1998
Bibliographic databases:
MSC: 42C15
Language: English
Original paper language: Russian
Citation: A. M. Sedletskii, “On the summability and convergence of non-harmonic Fourier series”, Izv. Math., 64:3 (2000), 583–600
Citation in format AMSBIB
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\by A.~M.~Sedletskii
\paper On the summability and convergence of non-harmonic Fourier series
\jour Izv. Math.
\yr 2000
\vol 64
\issue 3
\pages 583--600
\mathnet{http://mi.mathnet.ru/eng/im292}
\crossref{https://doi.org/10.1070/im2000v064n03ABEH000292}
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\zmath{https://zbmath.org/?q=an:0980.42025}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746981227}
Linking options:
  • https://www.mathnet.ru/eng/im292
  • https://doi.org/10.1070/im2000v064n03ABEH000292
  • https://www.mathnet.ru/eng/im/v64/i3/p151
  • This publication is cited in the following 7 articles:
    1. Gilbert Kerr, Nehemiah Lopez, Gilberto González-Parra, “Analytical Solutions of Systems of Linear Delay Differential Equations by the Laplace Transform: Featuring Limit Cycles”, MCA, 29:1 (2024), 11  crossref
    2. Michelle Sherman, Gilbert Kerr, Gilberto González-Parra, “Analytical solutions of linear delay-differential equations with Dirac delta function inputs using the Laplace transform”, Comp. Appl. Math., 42:6 (2023)  crossref
    3. Anton Baranov, Yurii Belov, Aleksei Kulikov, “Spectral synthesis for exponentials and logarithmic length”, Isr. J. Math., 250:1 (2022), 403  crossref
    4. Gilbert Kerr, Gilberto González-Parra, Michele Sherman, “A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations”, Applied Mathematics and Computation, 420 (2022), 126914  crossref
    5. Gilbert Kerr, Gilberto González-Parra, “Accuracy of the Laplace transform method for linear neutral delay differential equations”, Mathematics and Computers in Simulation, 197 (2022), 308  crossref
    6. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. II”, Journal of Mathematical Sciences, 130:6 (2005), 5083–5255  mathnet  crossref  mathscinet  zmath
    7. A. M. Sedletskii, “Bases of Exponentials in the Spaces $L^p(-\pi,\pi)$”, Math. Notes, 72:3 (2002), 383–397  mathnet  crossref  crossref  mathscinet  zmath  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:653
    Russian version PDF:280
    English version PDF:35
    References:99
    First page:1
     
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