Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Canonical systems
and transfer matrix-functions


Author: Alexander Sakhnovich
Journal: Proc. Amer. Math. Soc. 125 (1997), 1451-1455
MSC (1991): Primary 34L40, 47A10
DOI: https://doi.org/10.1090/S0002-9939-97-03749-0
MathSciNet review: 1371140
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The generalised Backlund-Darboux transform and its modifications are applied to the inverse spectral problems and problems on similarity of Hamiltonians for canonical systems.


References [Enhancements On Off] (What's this?)

  • 1. I. Gohberg and M. G. Krein, Theory and applications of Volterra operators in Hilbert space, Translated in: Transl. of Math. Monographs 24, Providence, Rhode Island, 1970. MR 41:9041
  • 2. L. de Branges, Hilbert spaces of entire functions, N.J., Prentice-Hall, 1968. MR 37:4590
  • 3. L. A. Sakhnovich, Factorisation problems and operator identities, Uspekhi Mat. Nauk 41 (1986), no. 1, 3-55. Translated in: Russian Math. Surv. 41 (1986).
  • 4. R. Miura (ed.), Backlund transformations, Lecture Notes in Math. 515, Springer, 1976 MR 58:15770
  • 5. A. L. Sakhnovich, Exact solutions of nonlinear equations and the method of operator identities, Lin. Alg. Appl. 182 (1993), 109-126. MR 94e:35044
  • 6. A. L. Sakhnovich, Dressing procedure for solutions of nonlinear equations and the method of operator identities, Inverse Pr. 10 (1994), 699-710. MR 95k:35175
  • 7. A. L. Sakhnovich, Iterated Darboux transform (the case of rational dependence on spectral parameter), Dokl. Akad. Nauk Ukraine (1995), no. 7, 24-27. CMP 96:06
  • 8. A. L. Sakhnovich, Spectral functions of a canonical system of order $2n$. Translated in: Math. USSR Sbornik 71 (1992), no. 2, 355-369.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34L40, 47A10

Retrieve articles in all journals with MSC (1991): 34L40, 47A10


Additional Information

Alexander Sakhnovich
Affiliation: Branch of Hydroacoustics, Marine Institute of Hydrophysics, Preobradjenskaya 3, 270100 Odessa, Ukraine
Address at time of publication: Faculteit Wiskunde en Informatica, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Email: sakhnov@cs.vu.nl

DOI: https://doi.org/10.1090/S0002-9939-97-03749-0
Keywords: Canonical system, transfer function, Backlund-Darboux transform, operator identity, spectral function
Received by editor(s): May 8, 1995
Received by editor(s) in revised form: August 4, 1995, and November 27, 1995
Additional Notes: The author’s research was supported by ISF grant UCX000.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society