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On the Riccati equations

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Abstract.

In this article we give, in terms of so-called Berezin symbols, some necessary conditions for the solvability of the Riccati equation \(XAX+XB-CX-D=0\) on the set \({\cal T}\) of all Toeplitz operators on the Hardy space \(H^2({\Bbb D})\).

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References

  • VM Adamjan H Langer C Tretter (2001) ArticleTitleExistence and uniqueness of contractive solutions of some Riccati equations J Funct Anal 179 448–473 Occurrence Handle0982.47019 Occurrence Handle10.1006/jfan.2000.3680 Occurrence Handle1809118

    Article  MATH  MathSciNet  Google Scholar 

  • EM Dynkin (1973) ArticleTitleWiener-Levy type theorems and estimation for the Wiener-Hopf operator Matem Issled Kishinev 8 IssueID3 14–25 Occurrence Handle336425

    MathSciNet  Google Scholar 

  • M Engliš (1995) ArticleTitleToeplitz operators and the Berezin transform on H 2 Linear Algebra Appl 223/224 171–204 Occurrence Handle10.1016/0024-3795(94)00056-J

    Article  Google Scholar 

  • Gambler LC (1977) A study of rational Toeplitz operators. State University of New York at Stony Brook: PhD Dissertation

  • C-H Guo P Lancaster (1998) ArticleTitleAnalysis and modification of Newton’s method for algebraic Riccati equations Math Comp 67 1089–1105 Occurrence Handle0903.65047 Occurrence Handle10.1090/S0025-5718-98-00947-8 Occurrence Handle1459388

    Article  MATH  MathSciNet  Google Scholar 

  • PR Halmos (1970) ArticleTitleTen problems in Hilbert space Bull Amer Math Soc 76 887–933 Occurrence Handle0204.15001 Occurrence Handle10.1090/S0002-9904-1970-12502-2 Occurrence Handle270173

    Article  MATH  MathSciNet  Google Scholar 

  • K Hoffman (1962) Banach Spaces of Analytic Functions Prentice-Hall Englewood Cliffs, NJ Occurrence Handle0117.34001

    MATH  Google Scholar 

  • MT Karaev (2002) ArticleTitleBerezin symbols and Schatten-von Neumann classes Math Notes 72 185–192 Occurrence Handle1026.47013 Occurrence Handle10.1023/A:1019893710815 Occurrence Handle1942546

    Article  MATH  MathSciNet  Google Scholar 

  • MT Karaev (2005) ArticleTitleOn some problems related to Berezin symbols C R Acad Sci Paris Ser I 340 715–718 Occurrence Handle1072.30008 Occurrence Handle2141055

    MATH  MathSciNet  Google Scholar 

  • P Lancaster L Rodman (1995) Algebraic Riccati equations Clarendon Oxford Occurrence Handle0836.15005

    MATH  Google Scholar 

  • H Langer C Tretter (1998) ArticleTitleSpectral decomposition of some nonselfadjoint block operator matrices J Operator Theory 39 339–359 Occurrence Handle0996.47006 Occurrence Handle1620503

    MATH  MathSciNet  Google Scholar 

  • H Langer C Tretter (2001) ArticleTitleDiagonalization of certain block operator matrices and applications to Dirac operators Operator Theory Adv Appl 122 331–358 Occurrence Handle1846064

    MathSciNet  Google Scholar 

  • H Langer A Markus V Matsaev C Tretter (2001) ArticleTitleA new concept for block operator matrices: the quadratic numerical range Linear Algebra Appl 330 89–112 Occurrence Handle0998.15035 Occurrence Handle10.1016/S0024-3795(01)00230-0 Occurrence Handle1826651

    Article  MATH  MathSciNet  Google Scholar 

  • R Mennicken A Motovilov (1999) ArticleTitleOperator interpretation of resonances arising in spectral problems of 2×2 operator matrices Math Nachr 201 117–181 Occurrence Handle0932.47010 Occurrence Handle1680916

    MATH  MathSciNet  Google Scholar 

  • A Motovilov (1995) ArticleTitleRemoval of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian J Math Phys 36 6647–6664 Occurrence Handle0884.47056 Occurrence Handle10.1063/1.531178 Occurrence Handle1359649

    Article  MATH  MathSciNet  Google Scholar 

  • VV Peller (1983) ArticleTitleInvariant subspaces of Toeplitz operators Zap Nauch Semin LOMI 126 170–179 Occurrence Handle0514.47019 Occurrence Handle697436

    MATH  MathSciNet  Google Scholar 

  • VV Peller (1987) ArticleTitleSpectrum, similarity and invariant subspaces of Toeplitz operators Math USSR Izv 29 133–144 Occurrence Handle0624.47017 Occurrence Handle10.1070/IM1987v029n01ABEH000963

    Article  MATH  Google Scholar 

  • K Zhu (1990) Operator theory in function spaces Marcel Dekker New York Occurrence Handle0706.47019

    MATH  Google Scholar 

  • N Zorboska (2003) ArticleTitleThe Berezin transform and radial operators Proc Amer Math Soc 131 793–800 Occurrence Handle1009.47015 Occurrence Handle10.1090/S0002-9939-02-06691-1 Occurrence Handle1937440

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Suleyman Demirel University, Isparta, Turkey

    M. T. Karaev

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  1. M. T. Karaev
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Author’s address: Department of Technical Programs, Isparta (MYO) Vocational School, Suleyman Demirel University, 32260 Isparta, Turkey

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Karaev, M. On the Riccati equations. Monatsh Math 155, 161–166 (2008). https://doi.org/10.1007/s00605-008-0542-4

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  • DOI: https://doi.org/10.1007/s00605-008-0542-4

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