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

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Show simple item record Barrios, Dolores López Lagomasino, Guillermo Martínez-Finkelshtein, Andrei Torrano, Emilio 2010-01-13T09:42:43Z 2010-01-13T09:42:43Z 1999
dc.identifier.bibliographicCitation Sbornik Mathematics c/c of Matematicheskii Sbornik, 1999, vol. 190, n. 4, p. 501-519
dc.identifier.issn 1064-5616
dc.description 19 pages, no figures.-- MSC1991 codes: Primary 47B99, 47A10, 40A15; Secondary 30B70.-- Originally published in Russian language by the Russian Academy of Mathematics in: Matematicheskii Sbornik 190(4): 23–42 (1999).
dc.description MR#: MR1702505 (2000e:47052)
dc.description Zbl#: Zbl 0935.47011
dc.description.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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Turpion Ltd.
dc.publisher Russian Academy of Sciences (RAS)
dc.rights © Turpion Ltd.
dc.subject.other Approximability of the resolvent
dc.subject.other Band matrix
dc.subject.other Bounded perturbations
dc.subject.other Eigenvalues of the tridiagonal matrix
dc.title Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1070/SM1999v190n04ABEH000389
dc.rights.accessRights openAccess
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