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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 2, Pages 50–62 (Mi faa295)  

This article is cited in 19 scientific papers (total in 19 papers)

Spectral Theory of a Class of Canonical Differential Systems

L. A. Sakhnovich

Ukranian State Academy of Telecommunication named after O. S. Popov

Abstract: The general spectral theory of canonical systems is used to study a generalized Krein system. Direct and inverse problems for this system are considered. In particular, some proofs are supplied for Krein's results published by him without proof.


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English version:
Functional Analysis and Its Applications, 2000, 34:2, 119–128

Bibliographic databases:

UDC: 517.9
Received: 03.08.1998

Citation: L. A. Sakhnovich, “Spectral Theory of a Class of Canonical Differential Systems”, Funktsional. Anal. i Prilozhen., 34:2 (2000), 50–62; Funct. Anal. Appl., 34:2 (2000), 119–128

Citation in format AMSBIB
\by L.~A.~Sakhnovich
\paper Spectral Theory of a Class of Canonical Differential Systems
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 2
\pages 50--62
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 2
\pages 119--128

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    This publication is cited in the following articles:
    1. Denisov, SA, “On the application of some of M. G. Krein's results to the spectral analysis of Sturm-Liouville operators”, Journal of Mathematical Analysis and Applications, 261:1 (2001), 177  crossref  mathscinet  zmath  isi  scopus
    2. Denisov, SA, “On the existence of the absolutely continuous component for the measure associated with some orthogonal systems”, Communications in Mathematical Physics, 226:1 (2002), 205  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Denisov, SA, “To the spectral theory of Krein systems”, Integral Equations and Operator Theory, 42:2 (2002), 166  crossref  mathscinet  zmath  isi  scopus
    4. Denisov, SA, “On the coexistence of absolutely continuous and singular continuous components of the spectral measure for some Sturm-Liouville operators with square summable potential”, Journal of Differential Equations, 191:1 (2003), 90  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Denisov, SA, “On the continuous analog of Rakhmanov's Theorem for orthogonal polynomials”, Journal of Functional Analysis, 198:2 (2003), 465  crossref  mathscinet  zmath  isi  scopus
    6. Denisov, SA, “On the absolutely continuous spectrum of Dirac operator”, Communications in Partial Differential Equations, 29:9–10 (2004), 1403  crossref  mathscinet  zmath  isi  scopus
    7. Arov, DZ, “The bitangential inverse spectral problem for canonical systems”, Journal of Functional Analysis, 214:2 (2004), 312  crossref  mathscinet  zmath  isi  scopus
    8. Denisov, SA, “On the existence of wave operators for some Dirac operators with square summable potential”, Geometric and Functional Analysis, 14:3 (2004), 529  crossref  mathscinet  zmath  isi  scopus
    9. Arov, DZ, “Direct and inverse problems for differential systems connected with Dirac systems and related factorization problems”, Indiana University Mathematics Journal, 54:6 (2005), 1769  crossref  mathscinet  zmath  isi
    10. Teplyaev, A, “A note on the theorems of M.G. Krein and L.A. Sakhnovich on continuous analogs of orthogonal polynomials on the circle”, Journal of Functional Analysis, 226:2 (2005), 257  crossref  mathscinet  zmath  isi  scopus
    11. Denisov, S, “On the singular spectrum of Schrodinger operators with decaying potential”, Transactions of the American Mathematical Society, 357:4 (2005), 1525  crossref  mathscinet  zmath  isi  scopus
    12. Arov D.Z., Dym H., “Strongly regular J-inner matrix-valued functions and inverse problems for canonical systems”, Recent Advances in Operator Theory and Its Applications: The Israel Gohberg Anniversary Volume, Operator Theory : Advances and Applications, 160, 2005, 101–160  crossref  mathscinet  zmath  isi
    13. Sakhnovich, L, “On Krein's differential system and its generalization”, Integral Equations and Operator Theory, 55:4 (2006), 561  crossref  mathscinet  zmath  isi  scopus
    14. Denisov, SA, “Schrodinger operators and associated hyperbolic”, Journal of Functional Analysis, 254:8 (2008), 2186  crossref  mathscinet  zmath  isi  scopus
    15. Killip, R, “Sum rules and spectral measures of Schrodinger operators with L-2 potentials”, Annals of Mathematics, 170:2 (2009), 739  crossref  mathscinet  zmath  isi  scopus
    16. Ginovyan M.S., Mikaelyan L.V., “Prediction Error for Continuous-Time Stationary Processes with Singular Spectral Densities”, Acta Applicandae Mathematicae, 110:1 (2010), 327–351  crossref  mathscinet  zmath  isi  scopus
    17. I. A. Taimanov, “Singulyarnye spektralnye krivye v konechnozonnom integrirovanii”, UMN, 66:1(397) (2011), 111–150  mathnet  crossref  mathscinet  zmath  elib
    18. Sakhnovich L., “Effective Construction of a Class of Positive Operators in Hilbert Space, Which Do Not Admit Triangular Factorization”, J. Funct. Anal., 263:3 (2012), 803–817  crossref  mathscinet  zmath  isi  scopus
    19. Arov D. Dym H., “Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems”, Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems, Operator Theory Advances and Applications, 266, Birkhauser Verlag Ag, 2018, 1–405  crossref  mathscinet  isi  scopus
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