Proceedings of the American Mathematical Society

Author(s): I. Egorova; L. Golinskii
Journal: Proc. Amer. Math. Soc. 133 (2005), 3635-3641.
MSC (2000): Primary 47B36; Secondary 47A55
Posted: June 28, 2005
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Abstract: We study spectrum inclusion regions for complex Jacobi matrices that are compact perturbations of the discrete Laplacian. The condition sufficient for the lack of a discrete spectrum for such matrices is given.

1.: Geronimo J.S. An upper bound on the number of eigenvalues of an infinite dimensional Jacobi matrix, J. Math. Phys. v.23, 1982, p.917-921. MR 0659989 (84i:47027)
2.: Geronimo J.S. On the spectra of infinite-dimensional Jacobi matrices, J. Approx. Theory v.53, 1988, p.251-265. MR 0947431 (90j:47037)
3.: Hundertmark D., Simon B. Lieb-Thirring inequalities for Jacobi matrices, J. Approx. Theory v.118, 2002, p.106-130. MR 1928259 (2003h:39016)
4.: Lyantse V.E. Nonselfadjoint discrete Schrödinger operator, DAN SSSR, v.173, no.6, 1967, p.1260-1263.
5.: Lyantse V.E. Spectrum and resolvent of a non-selfconjugate difference operator, Ukr. Math. J., v.20, no.4, 1968, p.489-503.
6.: Marchenko V. Sturm-Liouville operators and applications, Kiev, Naukova Dumka, 1977. MR 0481179 (58:1317)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B36, 47A55

I. Egorova
Affiliation: Institute of Low Temperatures, National Academy of Sciences of Ukraine, 61103 Kharkov, Ukraine
Email: egorova@ilt.kharkov.ua

L. Golinskii
Affiliation: Institute of Low Temperature Physics, National Academy of Sciences of Ukraine, 61103 Kharkov, Ukraine
Email: golinskii@ilt.kharkov.ua

DOI: 10.1090/S0002-9939-05-08181-5
PII: S 0002-9939(05)08181-5
Keywords: Complex Jacobi matrices, spectrum inclusion regions, Jost function, complex perturbation
Received by editor(s): August 18, 2004
Posted: June 28, 2005
Additional Notes: This work was partially supported by INTAS grant no. 03-51-6637.
Communicated by: Andreas Seeger
Copyright of article: Copyright 2005, American Mathematical Society

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