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 Mat. Zametki, 2018, Volume 104, Issue 1, Pages 3–10 (Mi mz11666)

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.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00333 Ministry of Education and Science of the Russian Federation ÍØ-6222.2018.1 This work was supported by the Russian Foundation for Basic Research under grant 18-01-00333 and by the Presidential Program for the State Support of Leading Scientific Schools under grant NSh-6222.2018.1.

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
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
\Bibitem{Bor18} \by P.~A.~Borodin \paper Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk \jour Mat. Zametki \yr 2018 \vol 104 \issue 1 \pages 3--10 \mathnet{http://mi.mathnet.ru/mz11666} \crossref{https://doi.org/10.4213/mzm11666} \elib{http://elibrary.ru/item.asp?id=35276445} \transl \jour Math. Notes \yr 2018 \vol 104 \issue 1 \pages 3--9 \crossref{https://doi.org/10.1134/S0001434618070015} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054366914} 

• http://mi.mathnet.ru/eng/mz11666
• https://doi.org/10.4213/mzm11666
• http://mi.mathnet.ru/eng/mz/v104/i1/p3

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