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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm4022https://doi.org/10.4213/mzm4022 https://www.mathnet.ru/eng/mzm/v83/i5/p643
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