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This article is cited in 2 scientific papers (total in 2 papers)
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
 Full text:
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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
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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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
 -
P. Chunaev, “Interpolation by generalized exponential sums with equal weights”, J. Approx. Theory, 254 (2020), UNSP 105397
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