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Mat. Zametki, 2008, Volume 83, Issue 5, Pages 643–649 (Mi mz4022)  

This article is cited in 9 scientific papers (total in 9 papers)

Approximation Properties of Sums of the Form $\sum_k\lambda_kh(\lambda_k z)$

V. I. Danchenko

Vladimir State University

Abstract: A method for approximating functions $f$ analytic in a neighborhood of the point $z=0$ by finite sums of the form $\sum_k\lambda_kh(\lambda_k z)$ is proposed, where $h$ is a chosen function analytic on the unit disk and the approximation is carried out by choosing the complex numbers $\lambda_k=\lambda_k(f)$. Some applications to numerical analysis are given.

Keywords: approximation of analytic functions, simple fractions, numerical derivation and integration, Mergelyan's theorem, maximum principle

DOI: https://doi.org/10.4213/mzm4022

Full text: PDF file (445 kB)
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English version:
Mathematical Notes, 2008, 83:5, 587–593

Bibliographic databases:

UDC: 517.538.5
Received: 05.02.2007

Citation: V. I. Danchenko, “Approximation Properties of Sums of the Form $\sum_k\lambda_kh(\lambda_k z)$”, Mat. Zametki, 83:5 (2008), 643–649; Math. Notes, 83:5 (2008), 587–593

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. N. Kondakova, “Interpolyatsiya naiprosteishimi drobyami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:2 (2009), 30–37  mathnet  crossref  elib
    2. P. V. Chunaev, “On a nontraditional method of approximation”, Proc. Steklov Inst. Math., 270 (2010), 278–284  mathnet  crossref  mathscinet  zmath  isi  elib
    3. P. V. Chunaev, “On the Extrapolation of Analytic Functions by Sums of the Form $\sum_k\lambda_k h(\lambda_k z)$”, Math. Notes, 92:5 (2012), 727–730  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Chunaev P. Danchenko V., “Approximation by amplitude and frequency operators”, J. Approx. Theory, 207 (2016), 1–31  crossref  mathscinet  zmath  isi  elib  scopus
    5. P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094  mathnet  crossref  crossref  adsnasa  isi  elib
    6. P. A. Borodin, “Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk”, Math. Notes, 104:1 (2018), 3–9  mathnet  crossref  crossref  isi  elib
    7. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    8. M. A. Komarov, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Math. Notes, 104:6 (2018), 848–858  mathnet  crossref  crossref  isi  elib
    9. M. A. Komarov, “On the rate of approximation in the unit disc of $H^1$-functions by logarithmic derivatives of polynomials with zeros on the boundary”, Izv. Math., 84:3 (2020), 437–448  mathnet  crossref  crossref  isi
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