|
This article is cited in 1 scientific paper (total in 1 paper)
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:
PDF file (460 kB)
 First page: PDF file
References:
PDF file
HTML file
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
\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}
Linking options:
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:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
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
|
| Number of views: |
| This page: | 277 | | References: | 29 | | First page: | 34 |
|
Terms of Use