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Russian Academy of Sciences. Sbornik. Mathematics, 1994, Volume 78, Issue 1, Pages 77–90
DOI: https://doi.org/10.1070/SM1994v078n01ABEH003459
(Mi sm957)
 

This article is cited in 15 scientific papers (total in 15 papers)

On a theorem of Adamian, Arov, and Krein

V. A. Prokhorov

Belarusian State University
References:
Abstract: Some questions in the theory of Hankel operators are considered. The basic results include a theorem generalizing the Adamian–Arov–Krein theorem for the case when the continuous function $f$ giving rise to the Hankel operator $A_f$ is defined on the boundary of a multiply connected domain $G$ bounded by finitely many closed analytic Jordan curves $\Gamma$. Estimates are obtained for the singular numbers $s_n$ of the Hankel operator $A_f$ in terms of the best approximation $\Delta_n$ of $f$ in the space $L_\infty(\Gamma)$ by functions belonging to the class $\mathcal R_n+E_\infty(G)$, where $\mathcal R_n$ is the class of rational functions of order at most $n$, and $E_\infty(G)$ is the Smirnov class of bounded analytic functions on $G$.
Received: 10.10.1991 and 25.06.1992
Bibliographic databases:
UDC: 517.5
MSC: Primary 47B35, 41A25, 41A20; Secondary 30E10, 30H05
Language: English
Original paper language: Russian
Citation: V. A. Prokhorov, “On a theorem of Adamian, Arov, and Krein”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 77–90
Citation in format AMSBIB
\Bibitem{Pro93}
\by V.~A.~Prokhorov
\paper On a theorem of Adamian, Arov, and Krein
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 1
\pages 77--90
\mathnet{http://mi.mathnet.ru//eng/sm957}
\crossref{https://doi.org/10.1070/SM1994v078n01ABEH003459}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1211367}
\zmath{https://zbmath.org/?q=an:0897.47021}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994NR97600005}
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  • https://doi.org/10.1070/SM1994v078n01ABEH003459
  • https://www.mathnet.ru/eng/sm/v184/i1/p89
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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