On conditions for the discreteness of the spectrum of a semiinfinite Jacobi matrix with zero diagonal

Ukrainian Mathematical Journal

Volumn 62, Issue 2, 2010, Pages 325-329

  Masmaliev, G M ^a   Khanmamedov, A Kh ^b  

^a BAKU STATE UNIVERSITY   (Azerbaijan)

^b INSTITUTE OF PHYSICS   (Azerbaijan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957775113     PISSN: 00415995     EISSN: 15739376     Source Type: Journal    
DOI: 10.1007/s11253-010-0356-0     Document Type: Article

References (9)

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2. G. Sh. Guseinov, "Definition of an infinite Jacobi matrix on the basis of two spectra," Mat. Zametki, 23, No. 5, 709-720 (1978).
3. F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York (1964).
4. A. M. Molchanov, "On the conditions of discreteness of the spectrum of self-adjoint differential equations," Tr. Mosk. Mat. Obshch., 2, 169-200 (1953).
5. V. Kirsh, S. A. Molchanov, and L. A. Pastur, "One-dimensional Schr̈odinger operator with unbounded potential: pure point spectrum," Funkts. Anal. Prilozhen., 24, No. 3, 14-25 (1990).
6. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1966).
7. Yu. M. Berezanskii, "One remark concerning a relatively loaded Toda chain," Ukr. Mat. Zh., 37, No. 3, 352-355 (1985).
8. A. G. Kostyuchenko and K. A. Mirzoev, "Generalized Jacobi matrices and indices of defect for ordinary differential operators with polynomial coefficients," Funkts. Anal. Prilozhen., 33, No. 1, 30-45 (1999).
9. P. O. Silva, Asymptotic Methods in the Spectral Analysis of Hermitian Jacobi Matrices [in Russian], Candidate-Degree Thesis (Physics and Mathematics), St. Petersburg (2003).