Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 6, Pages 125–144 (Mi izv8374)  

This article is cited in 1 scientific paper (total in 1 paper)

Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight

N. R. Ikonomova, R. K. Kovachevaa, S. P. Suetinb

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
b Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We obtain Nuttall's integral equation provided that the corresponding complex-valued function $\sigma(x)$ does not vanish and belongs to the Dini–Lipschitz class. Using this equation, we obtain a complex analogue of Bernshtein's classical asymptotic formulae for polynomials orthogonal on the closed unit interval $\Delta=[-1,1]$ with respect to a complex-valued weight $h(x)=\sigma(x)/\sqrt{1-x^2}$.

Keywords: orthogonal polynomials, Padé polynomials, strong asymptotics, Bernshtein's formula, Nuttall's method.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12430-офи-м-2
15-01-07531-a
Ministry of Education and Science of the Russian Federation НШ-2900.2014.1
This paper was written with the financial support of the RFBR (grants nos. 13-01-12430-ofi-m-2, 15-01-07531-a) and the President's Programme ‘Support of Leading Scientific Schools’ (grant no. NSh-2900.2014.1).


DOI: https://doi.org/10.4213/im8374

Full text: PDF file (702 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2015, 79:6, 1215–1234

Bibliographic databases:

UDC: 517.53
MSC: 30B70, 33D45, 41A21, 41A25, 41A60, 42C05
Received: 01.04.2015

Citation: N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. RAN. Ser. Mat., 79:6 (2015), 125–144; Izv. Math., 79:6 (2015), 1215–1234

Citation in format AMSBIB
\Bibitem{IkoKovSue15}
\by N.~R.~Ikonomov, R.~K.~Kovacheva, S.~P.~Suetin
\paper Nuttall's integral equation and Bernshtein's asymptotic formula for a~complex weight
\jour Izv. RAN. Ser. Mat.
\yr 2015
\vol 79
\issue 6
\pages 125--144
\mathnet{http://mi.mathnet.ru/izv8374}
\crossref{https://doi.org/10.4213/im8374}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438467}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015IzMat..79.1215I}
\elib{https://elibrary.ru/item.asp?id=24850004}
\transl
\jour Izv. Math.
\yr 2015
\vol 79
\issue 6
\pages 1215--1234
\crossref{https://doi.org/10.1070/IM2015v079n06ABEH002778}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000371441400005}
\elib{https://elibrary.ru/item.asp?id=27074680}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960491456}


Linking options:
  • http://mi.mathnet.ru/eng/izv8374
  • https://doi.org/10.4213/im8374
  • http://mi.mathnet.ru/eng/izv/v79/i6/p125

    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. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:442
    Full text:109
    References:33
    First page:18

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