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Sbornik: Mathematics, 1999, Volume 190, Issue 4, Pages 501–519
DOI: https://doi.org/10.1070/sm1999v190n04ABEH000389
(Mi sm389)
 

This article is cited in 9 scientific papers (total in 9 papers)

Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

D. Barriosa, G. L. Lopesb, A. Martínez-Finkelshteinc, E. Torranod

a University of the Basque Country
b Carlos III University of Madrid
c Universidad de Almería
d Polytechnic University of Madrid
References:
Abstract: The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established.
Received: 25.12.1995 and 15.06.1998
Bibliographic databases:
UDC: 517.5
MSC: Primary 47B99, 47A10, 40A15; Secondary 30B70
Language: English
Original paper language: Russian
Citation: D. Barrios, G. L. Lopes, A. Martínez-Finkelshtein, E. Torrano, “Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions”, Sb. Math., 190:4 (1999), 501–519
Citation in format AMSBIB
\Bibitem{BarLopMar99}
\by D.~Barrios, G.~L.~Lopes, A.~Mart{\'\i}nez-Finkelshtein, E.~Torrano
\paper Finite-dimensional approximations of the~resolvent of an~infinite band matrix and continued fractions
\jour Sb. Math.
\yr 1999
\vol 190
\issue 4
\pages 501--519
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  • https://doi.org/10.1070/sm1999v190n04ABEH000389
  • https://www.mathnet.ru/eng/sm/v190/i4/p23
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:649
    Russian version PDF:196
    English version PDF:17
    References:59
    First page:1
     
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