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., 2002, Volume 193, Number 9, Pages 63–92 (Mi msb679)  

This article is cited in 4 scientific papers (total in 4 papers)

Padé approximants for entire functions with regularly decreasing Taylor coefficients

V. N. Rusak, A. P. Starovoitov

Belarusian State University

Abstract: For a class of entire functions the asymptotic behaviour of the Hadamard determinants $D_{n,m}$ as $0\leqslant m\leqslant m(n)\to\infty$ and $n\to\infty$ is described. This enables one to study the behaviour of parabolic sequences from Padé and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences $\{(n,m(n))\}$ in certain classes of entire functions (with regular Taylor coefficients) the Padé approximants $\{\pi_{n,m(n)}\}$, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set $D=ż:|z|\leqslant 1\}$ with asymptotically best rate.

DOI: https://doi.org/10.4213/sm679

Full text: PDF file (396 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2002, 193:9, 1303–1332

Bibliographic databases:

UDC: 517.51+517.53
MSC: Primary 41A21, 41A20; Secondary 30D15
Received: 28.09.2001 and 27.05.2002

Citation: V. N. Rusak, A. P. Starovoitov, “Padé approximants for entire functions with regularly decreasing Taylor coefficients”, Mat. Sb., 193:9 (2002), 63–92; Sb. Math., 193:9 (2002), 1303–1332

Citation in format AMSBIB
\Bibitem{RusSta02}
\by V.~N.~Rusak, A.~P.~Starovoitov
\paper Pad\'e approximants for entire functions with regularly decreasing Taylor coefficients
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 9
\pages 63--92
\mathnet{http://mi.mathnet.ru/msb679}
\crossref{https://doi.org/10.4213/sm679}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1936857}
\zmath{https://zbmath.org/?q=an:1047.41012}
\transl
\jour Sb. Math.
\yr 2002
\vol 193
\issue 9
\pages 1303--1332
\crossref{https://doi.org/10.1070/SM2002v193n09ABEH000679}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000180375800003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036767858}


Linking options:
  • http://mi.mathnet.ru/eng/msb679
  • https://doi.org/10.4213/sm679
  • http://mi.mathnet.ru/eng/msb/v193/i9/p63

    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. A. P. Starovoitov, N. A. Starovoitova, “Padé approximants of the Mittag-Leffler functions”, Sb. Math., 198:7 (2007), 1011–1023  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. P. Starovoitov, N. A. Starovoitova, “On the Asymptotics of the Rows of the Padé Table of Analytic Functions with Logarithmic Branch Points”, Math. Notes, 84:3 (2008), 379–388  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Yu. A. Labych, A. P. Starovoitov, “Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients”, Sb. Math., 200:7 (2009), 1051–1074  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:326
    Full text:108
    References:35
    First page:1

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