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

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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} λ_{k} h (λ_{k} z)

$\sum_k\lambda_kh(\lambda_k z)$

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

$f$ analytic in a neighborhood of the point

z = 0

$z=0$ by finite sums of the form

\sum_{k} λ_{k} h (λ_{k} z)

$\sum_k\lambda_kh(\lambda_k z)$ is proposed, where

h

$h$ is a chosen function analytic on the unit disk and the approximation is carried out by choosing the complex numbers

λ_{k} = λ_{k} (f)

$\lambda_k=\lambda_k(f)$ . 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} λ_{k} h (λ_{k} z)

$\sum_k\lambda_kh(\lambda_k z)$ ”, Mat. Zametki, 83:5 (2008), 643–649; Math. Notes, 83:5 (2008), 587–593

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm4022

https://doi.org/10.4213/mzm4022

https://www.mathnet.ru/eng/mzm/v83/i5/p643

This publication is cited in the following 15 articles:

P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
M. A. Komarov, “Convergence rate of one class of differentiating sums”, Ufa Math. J., 13:4 (2021), 41–49
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
Chunaev P., “Interpolation By Generalized Exponential Sums With Equal Weights”, J. Approx. Theory, 254 (2020), UNSP 105397
Komarov M.A., “Rate of Approximation of Zf'(Z) By Special Sums Associated With the Zeros of the Bessel Polynomials”, Indag. Math.-New Ser., 31:3 (2020), 450–457
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
V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Russian Math. (Iz. VUZ), 62:12 (2018), 6–41
M. A. Komarov, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Math. Notes, 104:6 (2018), 848–858
P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094
Yu. M. Nigmatyanova, “Numerical Analysis of the Method of Differentiation by Means of Real h-Sums”, J Math Sci, 224:5 (2017), 735
Chunaev P. Danchenko V., “Approximation by amplitude and frequency operators”, J. Approx. Theory, 207 (2016), 1–31
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
V. I. Danchenko, P. V. Chunaev, “Approximation by simple partial fractions and their generalizations”, J Math Sci, 176:6 (2011), 844
P. V. Chunaev, “On a nontraditional method of approximation”, Proc. Steklov Inst. Math., 270 (2010), 278–284
E. N. Kondakova, “Interpolyatsiya naiprosteishimi drobyami”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 9:2 (2009), 30–37

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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