A spectral analysis for self-adjoint operators generated by a class of second order difference equations

Journal of Mathematical Analysis and Applications

Volumn 197, Issue 1, 1996, Pages 267-285

  Clark, S L ^a  

^a MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0029715611     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0020     Document Type: Article

References (21)

1. 1. T. ASAHI, Spectral theory of the difference equations, Prog. Theoret. Phys. Suppl. 36 (1966), 55-96.
2. 2. F. V. ATKINSON, "Discrete and Continuous Boundary Problems," Academic Press, New York, 1964.
3. 3. H. BEHNCKE, Absolute continuity of Hamiltonians with von Neumann-Wigner potentials, Proc. Amer. Math. Soc. 111 (1991), 373-384.
4. 4. H. BEHNCKE, Absolute continuity of Hamiltonians with von Neumann-Wigner potentials, II, Manuscripta Math. 71 (1991), 163-181.
5. 5. C. BENNEWITZ, Spectral asymptotics for Sturm-Liouville equations, Proc. London Math. Soc. 59, No. 3 (1989), 238-294.
6. 6. R. R. DELRIO CASTILLO, On conditions which guarantee stability of the absolutely continuous spectrum of ordinary differential operators, Quart. J. Math. Oxford 39, No. 2 (1988), 269-280.
7. 7. S. L. CLARK, A criterion for absolute continuity of the continuous spectrum of a Hamiltonian system, J. Math. Anal. Appl. 151, No. 1 (1990), 108-128.
8. 8. S. L. CLARK, On the absolutely continuous spectrum of a vector-matrix Dirac system, Proc. Roy. Soc. Edinburgh, to appear.
9. 9. S. L. CLARK AND D. B. HINTON, Strong nonsubordinacy and absolutely continuous spectra for Sturm-Liouville equations, Differential Integral Equations 6, No. 3 (1993), 573-586.
10. 10. J. DOMBROWSKI, Tridiagonal matrix representations of cyclic self adjoint operators, II, Pacific J. Math. 120, No. 1 (1985), 47-53.
11. 11. J. DOMBROWSKI, Cyclic operators, commutators, and absolutely continuous measures, Proc. Amer. Math. Soc. 100, No. 3 (1987), 457-463.
12. 12. J. DOMBROWSKI, Spectral measures, orthogonal polynomials, and absolute continuity, SIAM J. Math. Anal. 19, No. 4 (1988), 938-943.
13. 13. J. DOMBROWSKI AND P. NEVAI, Orthogonal polynomials, measures and recurrence relations, SIAM J. Math. Anal. 17, No. 3 (1986), 752-759.
14. 14. D. J. GILBERT AND D. B. PEARSON, On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators, J. Math. Anal. Appl. 128 (1987), 30-56.
15. 15. D. J. GILBERT, On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints, Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 213-229.
16. 17. D. B. HINTON AND R. T. LEWIS, Spectral analysis of second order difference equations, J. Math. Anal. Appl. 63, No. 2 (1978), 421-438.
17. 19. F. MANTLIK AND A. SCHNEIDER, Note on the absolutely continuous spectrum of Sturm-Liouville operators, preprint.
18. 20. A. MATé AND P. NEVAI, Orthogonal polynomials and absolutely continuous measures, in "Approximation Theory" (C. K. Chui and L. L. Shumakar, Eds.), Vol. IV, pp. 611-617, Academic Press, New York, 1983.
19. 21. A. B. MINGARELLI, "Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions," Lecture Notes in Mathematics, Vol. 989, Springer-Verlag, Berlin, 1983.
20. 22. D. SMITH, On the spectral analysis of self-adjoint operators generated by second order difference equations, Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 139-151.
21. 23. G. STOLZ, Spectral theory for slowly oscillating potentials. I. Jacobi matrices, preprint.