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Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk
P. A. Borodin Lomonosov Moscow State University
Abstract:
Given a function $h$ analytic in the unit disk $D$, we study the density in the space $A(D)$ of functions analytic inside $D$ of the set $S(h,E)$ of sums of the form $\sum_k\lambda_kh(\lambda_kz)$ with parameters $\lambda_k\in E$, where $E$ is a compact subset of $\overline D$. It is proved, in particular, that if the compact set $E$ “surrounds” the point $0$ and all Taylor coefficients of the function $h$ are nonzero, then $S(h,E)$ is dense in $A(D)$.
Keywords:
approximation, analytic function, density, $h$-sum.
DOI:
https://doi.org/10.4213/mzm11666
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English version:
Mathematical Notes, 2018, 104:1, 3–9
Bibliographic databases:
UDC:
517.538.5 Received: 06.05.2017 Revised: 16.10.2017
Citation:
P. A. Borodin, “Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk”, Mat. Zametki, 104:1 (2018), 3–10; Math. Notes, 104:1 (2018), 3–9
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz11666https://doi.org/10.4213/mzm11666 http://mi.mathnet.ru/eng/mz/v104/i1/p3
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