Geodesic
Approximation Properties of Sums of the Form $\sum_k\lambda_kh(\lambda_k z)$
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 643-649

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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, numerical derivation and integration, Mergelyan's theorem, maximum principle.
Mots-clés : simple fractions 
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     author = {V. I. Danchenko},
     title = {Approximation {Properties} of {Sums} of the {Form} $\sum_k\lambda_kh(\lambda_k z)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--649},
     publisher = {mathdoc},
     volume = {83},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a0/}
}
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V. I. Danchenko. Approximation Properties of Sums of the Form $\sum_k\lambda_kh(\lambda_k z)$. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 643-649. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a0/