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., 2013, Volume 204, Number 2, Pages 39–72 (Mi msb8099)  

This article is cited in 17 scientific papers (total in 17 papers)

Convergence of multipoint Padé approximants of piecewise analytic functions

V. I. Buslaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The behaviour as $n\to\infty$ of multipoint Padé approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Padé approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Padé approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points.
Bibliography: 11 titles.

Keywords: rational approximation, orthogonal polynomials, Padé approximants, convergence in capacity, asymptotic behaviour of poles.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00330
Ministry of Education and Science of the Russian Federation НШ-4664.2012.1


DOI: https://doi.org/10.4213/sm8099

Full text: PDF file (719 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:2, 190–222

Bibliographic databases:

UDC: 517.53
MSC: Primary 41A21; Secondary 31A15
Received: 26.12.2011 and 06.12.2012

Citation: V. I. Buslaev, “Convergence of multipoint Padé approximants of piecewise analytic functions”, Mat. Sb., 204:2 (2013), 39–72; Sb. Math., 204:2 (2013), 190–222

Citation in format AMSBIB
\Bibitem{Bus13}
\by V.~I.~Buslaev
\paper Convergence of multipoint Pad\'e approximants of piecewise analytic functions
\jour Mat. Sb.
\yr 2013
\vol 204
\issue 2
\pages 39--72
\mathnet{http://mi.mathnet.ru/msb8099}
\crossref{https://doi.org/10.4213/sm8099}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3087097}
\zmath{https://zbmath.org/?q=an:06197061}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013SbMat.204..190B}
\elib{http://elibrary.ru/item.asp?id=19066616}
\transl
\jour Sb. Math.
\yr 2013
\vol 204
\issue 2
\pages 190--222
\crossref{https://doi.org/10.1070/SM2013v204n02ABEH004297}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000317574500003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876701744}


Linking options:
  • http://mi.mathnet.ru/eng/msb8099
  • https://doi.org/10.4213/sm8099
  • http://mi.mathnet.ru/eng/msb/v204/i2/p39

    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

    This publication is cited in the following articles:
    1. V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Method of interior variations and existence of $S$-compact sets”, Proc. Steklov Inst. Math., 279 (2012), 25–51  mathnet  crossref  mathscinet  isi  elib
    2. A. V. Komlov, S. P. Suetin, “An asymptotic formula for a two-point analogue of Jacobi polynomials”, Russian Math. Surveys, 68:4 (2013), 779–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. E. A. Rakhmanov, S. P. Suetin, “The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. I. Buslaev, S. P. Suetin, “Existence of compact sets with minimum capacity in problems of rational approximation of multivalued analytic functions”, Russian Math. Surveys, 69:1 (2014), 159–161  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. R. K. Kovacheva, S. P. Suetin, “Distribution of zeros of the Hermite–Padé polynomials for a system of three functions, and the Nuttall condenser”, Proc. Steklov Inst. Math., 284 (2014), 168–191  mathnet  crossref  crossref  isi  elib  elib
    6. V. I. Buslaev, S. P. Suetin, “An extremal problem in potential theory”, Russian Math. Surveys, 69:5 (2014), 915–917  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. V. Komlov, S. P. Suetin, “Strong asymptotics of two-point Padé approximants for power-like multivalued functions”, Dokl. Math., 89:2 (2014), 165–168  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. V. I. Buslaev, “Convergence of $m$-point Padé approximants of a tuple of multivalued analytic functions”, Sb. Math., 206:2 (2015), 175–200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. V. I. Buslaev, S. P. Suetin, “On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials”, Proc. Steklov Inst. Math., 290:1 (2015), 256–263  mathnet  crossref  crossref  isi  elib  elib
    10. V. I. Buslaev, “Capacity of a compact set in a logarithmic potential field”, Proc. Steklov Inst. Math., 290:1 (2015), 238–255  mathnet  crossref  crossref  isi  elib  elib
    11. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Sb. Math., 206:12 (2015), 1707–1721  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. A. V. Komlov, S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials”, Russian Math. Surveys, 70:6 (2015), 1179–1181  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. V. I. Buslaev, S. P. Suetin, “On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions”, J. Approx. Theory, 206:SI (2016), 48–67  crossref  mathscinet  zmath  isi  scopus
    15. A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Asymptotics of type I Hermite–Padé polynomials for semiclassical functions”, Modern trends in constructive function theory, Contemp. Math., 661, ed. D. Hardin, D. Lubinsky, B. Simanek, Amer. Math. Soc., Providence, RI, 2016, 199–228  crossref  mathscinet  zmath  isi
    16. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:479
    Full text:125
    References:42
    First page:22

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019