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., 2018, Volume 209, Number 3, Pages 102–137 (Mi msb8724)  

This article is cited in 2 scientific papers (total in 2 papers)

High-order recurrence relations, Hermite-Padé approximation and Nikishin systems

D. Barrios Rolaníaa, J. S. Geronimob, G. López Lagomasinoc

a Hidráulica y Ordenación del Territorio, Universidad Politécnica de Madrid, Madrid, Spain
b Department of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA
c Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain

Abstract: The study of sequences of polynomials satisfying high-order recurrence relations is connected with the asymptotic behaviour of multiple orthogonal polynomials, the convergence properties of type II Hermite-Padé approximation and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin-type system of measures.
Bibliography: 20 titles.

Keywords: high-order recurrence relation, Hermite-Padé approximation, multiple orthogonality, Nikishin system.

Funding Agency Grant Number
Ministerio de Economía y Competitividad MTM2014-54053-P
MTM2015-65888-C4-2
Simons Foundation

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8724

Full text: PDF file (995 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2018, 209:3, 385–420

Bibliographic databases:

UDC: 517.538.3+517.538.5
MSC: Primary 30E10, 42C05; Secondary 41A20
Received: 26.04.2016 and 20.01.2017

Citation: D. Barrios Rolanía, J. S. Geronimo, G. López Lagomasino, “High-order recurrence relations, Hermite-Padé approximation and Nikishin systems”, Mat. Sb., 209:3 (2018), 102–137; Sb. Math., 209:3 (2018), 385–420

Citation in format AMSBIB
\Bibitem{BarGerLop18}
\by D.~Barrios Rolan{\'\i}a, J.~S.~Geronimo, G.~L\'opez Lagomasino
\paper High-order recurrence relations, Hermite-Pad\'e approximation and Nikishin systems
\jour Mat. Sb.
\yr 2018
\vol 209
\issue 3
\pages 102--137
\mathnet{http://mi.mathnet.ru/msb8724}
\crossref{https://doi.org/10.4213/sm8724}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018SbMat.209..385B}
\elib{http://elibrary.ru/item.asp?id=32428135}
\transl
\jour Sb. Math.
\yr 2018
\vol 209
\issue 3
\pages 385--420
\crossref{https://doi.org/10.1070/SM8724}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000432853500004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048123128}


Linking options:
  • http://mi.mathnet.ru/eng/msb8724
  • https://doi.org/10.4213/sm8724
  • http://mi.mathnet.ru/eng/msb/v209/i3/p102

    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. 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
    2. S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:265
    References:27
    First page:26

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