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Matematicheskie Zametki, 2008, Volume 83, Issue 5, Pages 643–649
DOI: https://doi.org/10.4213/mzm4022 (Mi mzm4022) 		 
This article is cited in 15 scientific papers (total in 15 papers)

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

V. I. Danchenko

Vladimir State University
Full-text PDF (445 kB) Citations (15)
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DOI: https://doi.org/10.4213/mzm4022
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.
Received: 05.02.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 5, Pages 587–593
DOI: https://doi.org/10.1134/S0001434608050015
Bibliographic databases:
UDC: 517.538.5
Language: Russian
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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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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