On the existence of the absolutely continuous component for the measure associated with some orthogonal systems

Communications in Mathematical Physics

Volumn 226, Issue 1, 2002, Pages 205-220

  Denisov, Sergey A ^a,b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036002926     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200598     Document Type: Article

References (19)

1. Akhiezer, N.I., Rybalko, A.M.: On the continuous analogues of polinomials orthogonal on the unit circle. Ukranian Math. J. 20, no. 1, 3-24 (1968)
2. Deift, P., Killip, R.: On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials. Commun. Math. Phys. 203, 341-347 (1999)
3. Denisov, S.A.: To the spectral theory of Krein systems (to appear in Integral Equations Operator Theory)
4. Denisov, S.A.: On the application of some M.G. Krein's results to the spectral analysis of Sturm-Liouville operators. Journal of Math. Analysis and Applications 261, 1, 171-191 (2001)
5. Gilbert, D.J., Pearson, D.B.: On the subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators. J. Math. Anal. 128, 30-56 (1987)
6. Krein, M.G.: Continuous analogues of propositions on polynomials orthogonal on the unit circle. Dokl. Akad. Nauk SSSR 105, 637-640 (1955)
7. Molchanov, S., Novitskii, M., Vainberg, B.: First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator. Commun. Math. Phys. 216, 195-213 (2001)
8. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. 1. London: Academic Press, 1972
9. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. 3. London: Academic Press, 1979
10. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. 4. London: Academic Press, 1978
11. Rybalko, A.M.: On the theory of continual analogues of orthogonal polynomials. Teor. Funktsii, Funktsional. Anal. i Prilozhen. 3, 42-60 (1966)
12. Sakhnovich, L.A.: Spectral theory of a class of canonical systems. Funct. Anal. Appl. 34, no. 2, 119-129 (2000)
13. Sakhnovich, L.A.: On a class of canonical systems on half-axis. Integral Equations Operator Theory. 31, 92-112 (1998)
14. Sakhnovich, L.A.: Spectral theory of canonical differential systems: method of operator identities. Oper. Theory, Adv. and Applications. Vol. 107. Basel, Boston: Birkhäuser Verlag, 1999
15. Simon, B.: Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators. Proc. Amer. Math. Soc. 124, no. 11, 3361-3369 (1996)
16. Simon, B., Spencer, T.: Trace class perturbations and the absence of absolutely continuous spectra. Commun. Math. Phys. 125, 113-125 (1989)
17. Stolz, G.: Spectral theory for slowly oscillating potentials II. Schrödinger operators. Math. Nachr. 183, 275-294 (1997)
18. von Neumann, J., Wigner, E.: Über merkwürdige diskrete Eigenwerte. Z. Phys. 30, 465-467 (1929)
19. Teplyaev, A.V.: continuous analogues of random polynomials that are orthogonal on the circle. Theory Probab. Appl. 39, no. 3, 476-489 (1994)