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 Tr. Mat. Inst. Steklova, 2010, Volume 270, Pages 281–287 (Mi tm3020)

On a nontraditional method of approximation

P. V. Chunaev

Chair of Functional Analysis and Its Applications, Vladimir State University, Vladimir, Russia

Abstract: We study the approximation of functions $f(z)$ that are analytic in a neighborhood of zero by finite sums of the form $H_n(z)=H_n(h,f,\{\lambda_k\};z)=\sum_{k=1}^n\lambda_kh(\lambda_kz)$, where $h$ is a fixed function that is analytic in the unit disk $|z|<1$ and the numbers $\lambda_k$ (which depend on $h,f$, and $n$) are calculated by a certain algorithm. An exact value of the radius of the convergence $H_n(z)\to f(z)$, $n\to\infty$, and an order-sharp estimate for the rate of this convergence are obtained; an application to numerical analysis is given.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 270, 278–284

Bibliographic databases:

UDC: 517.538.5

Citation: P. V. Chunaev, “On a nontraditional method of approximation”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 281–287; Proc. Steklov Inst. Math., 270 (2010), 278–284

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. 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
2. Chunaev P., “Least Deviation of Logarithmic Derivatives of Algebraic Polynomials From Zero”, J. Approx. Theory, 185 (2014), 98–106
3. Chunaev P., Danchenko V., “Approximation by amplitude and frequency operators”, J. Approx. Theory, 207 (2016), 1–31
4. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49
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