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

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URI: https://hdl.handle.net/10016/6357
ISSN: 1064-5616
DOI: 10.1070/SM1999v190n04ABEH000389
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finite_lagomasino_sm_1999_ps.pdf (184.59 KB)
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1999
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Turpion Ltd.
Russian Academy of Sciences (RAS)
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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.
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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).
MR#: MR1702505 (2000e:47052)
Zbl#: Zbl 0935.47011
Keywords
Approximability of the resolvent, Band matrix, Bounded perturbations, Eigenvalues of the tridiagonal matrix
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Sbornik Mathematics c/c of Matematicheskii Sbornik, 1999, vol. 190, n. 4, p. 501-519
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