On the coexistence of absolutely continous and singular continous components of the spectral measure for some Sturm-Liouville operators with square summable potential

Journal of Differential Equations

Volumn 191, Issue 1, 2003, Pages 90-104

  Denisov, Sergey A ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038626232     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(02)00145-6     Document Type: Article

References (20)

1. F.V. Atkinson, Discrete and Continuous Boundary Value Problem, Academic Press, New York, 1964.
2. P. Deift, E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979) 121-251.
3. P. Deift, R. Killip, On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials, Comm. Math. Phys. 203 (1999) 341-347.
4. S.A. Denisov, On the application of some M.G.Krein's results to the spectral analysis of Sturm-Liouville operators, J. Math. Anal. Appl. 261 (1) (2001) 177-191.
5. S.A. Denisov, To the Spectral Theory of Krein Systems, Integral Equations Operator Theory 42 (2) (2002) 166-173.
6. R.K. Dodd, J.C. Eilenbeck, J.D. Gibbon, H.C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, London, New York, 1982.
7. Ya. L. Geronimus, Polynomials orthogonal on the segment and unit circle, Fizmatgiz, Moscow, 1958 (in Russian).
8. R. Killip, B. Simon, Sum rules for Jacoby matrices and their applications to spectral theory, preprint.
9. A. Kiselev, Imbedded singular continuous spectrum for Schrödinger operators, preprint.
10. M.G. Krein, Continuous analogues of propositions on polynomials orthogonal on the unit circle, Dokl. Akad. Nauk SSSR 105 (1955) 637-640.
11. M.G. Krein, Integral equations on the half-line with a kernel depending on the difference of the arguments, Uspehi Mat. Nauk 13(5)(83) (1958) 3-120 (in Russian)
12. M.G. Krein, Theory and Applications of Volterra Operators in Hilbert Space, Translations of Mathematical Monographs, Vol. 24, Amer. Math. Soc. Providence, RI, 1970.
13. M.G. Krein, On determination of the potential of a particle from its S-function, Dokl. Akad. Nauk SSSR 105 (1955) 433-436.
14. B.M. Levitan, Inverse Sturm-Liouville problems, Zeist, 1987.
15. S. Molchanov, M. Novitskii, B. Vainberg, First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator, Comm. Math. Phys. 216(2001) 195-213.
16. A.M. Rybalko, On the theory of continual analogues of orthogonal polynomials, Teor. Funktsii Funktsional. Anal. i Prilozhen. 3 (1966) 42-60.
17. L.A. Sakhnovich, Spectral theory of a class of canonical systems, Funct. Anal. Appl. 34 (2) (2000) 119-129.
18. B. Simon, Schrödinger operator in the twenty-first century, in: A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (Eds.), Mathematical Physics, 2000, Imperial College Press, London, 2000, pp. 283-288.
19. J. Sylvester, D. Winebrenner, Linear and nonlinear inverse scattering, SIAM J. Appl. Math. 59 (2) (1999) 669-699.
20. A.V. Teplyaev, Continuous analogues of random polynomials that are orthogonal on the circle, Theory Probab. Appl. 39 (3) (1994) 476-489.