|
Canonical systems and transfer matrix-functions
Author(s):
Alexander
Sakhnovich
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1451-1455.
MSC (1991):
Primary 34L40, 47A10
MathSciNet review:
1371140
Retrieve article in:
PDF
This article is available free of charge
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:
- 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
 . 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:
10.1090/S0002-9939-97-03749-0
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
|
