Matematicheskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2020, Volume 211, Number 12, Pages 3–48 (Mi msb9366)  

Necessary and sufficient conditions for extending a function to a Schur function

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: A criterion for a function given by its values (with multiplicities) at a sequence of points in the disc $\mathbb D=\{|z|<1\}$ to extend to a holomorphic function in $\mathbb D$ with modulus at most $1$ is stated and proved. In the case when the function is defined by the values of its derivatives at $z=0$, this coincides with Schur's well-known criterion.
Bibliography: 16 titles.

Keywords: continued fractions, Schur functions, Hankel determinants.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614).


DOI: https://doi.org/10.4213/sm9366

Full text: PDF file (792 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2020, 211:12, 1660–1703

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E05, 30H05; Secondary 30B70
Received: 23.12.2019 and 28.09.2020

Citation: V. I. Buslaev, “Necessary and sufficient conditions for extending a function to a Schur function”, Mat. Sb., 211:12 (2020), 3–48; Sb. Math., 211:12 (2020), 1660–1703

Citation in format AMSBIB
\Bibitem{Bus20}
\by V.~I.~Buslaev
\paper Necessary and sufficient conditions for~extending a~function to a~Schur function
\jour Mat. Sb.
\yr 2020
\vol 211
\issue 12
\pages 3--48
\mathnet{http://mi.mathnet.ru/msb9366}
\crossref{https://doi.org/10.4213/sm9366}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4045696}
\elib{https://elibrary.ru/item.asp?id=46744476}
\transl
\jour Sb. Math.
\yr 2020
\vol 211
\issue 12
\pages 1660--1703
\crossref{https://doi.org/10.1070/SM9366}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000617465800001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85101058084}


Linking options:
  • http://mi.mathnet.ru/eng/msb9366
  • https://doi.org/10.4213/sm9366
  • http://mi.mathnet.ru/eng/msb/v211/i12/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:165
    References:13
    First page:13

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021