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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Canonical systems and transfer matrix-functions
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by Alexander Sakhnovich PDF
Proc. Amer. Math. Soc. 125 (1997), 1451-1455 Request permission

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
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  • Louis de Branges, Hilbert spaces of entire functions, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1968. MR 0229011
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  • Alexander Sakhnovich, Exact solutions of nonlinear equations and the method of operator identities, Linear Algebra Appl. 182 (1993), 109–126. MR 1207078, DOI 10.1016/0024-3795(93)90495-A
  • A. L. Sakhnovich, Dressing procedure for solutions of nonlinear equations and the method of operator identities, Inverse Problems 10 (1994), no. 3, 699–710. MR 1278583
  • A. L. Sakhnovich, Iterated Darboux transform (the case of rational dependence on spectral parameter), Dokl. Akad. Nauk Ukraine (1995), no. 7, 24–27.
  • A. L. Sakhnovich, Spectral functions of a canonical system of order $2n$. Translated in: Math. USSR Sbornik 71 (1992), no. 2, 355–369.
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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
  • 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 1997 American Mathematical Society
  • 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