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2001 | 11 | 1 | 35-53
Tytuł artykułu

Reproducing kernels and Riccati equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.
Rocznik
Tom
11
Numer
1
Strony
35-53
Opis fizyczny
Daty
wydano
2001
otrzymano
2000-09-01
poprawiono
2001-01-01
Twórcy
autor
  • Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Bibliografia
  • Alpay D. and Dym H. (1986): On applications of reproducingkernel spaces to the Schur algorithm and rational J unitaryfactorization, In: Schur Methods in Operator Theory and Signal Processing (I. Gohberg, Eds.). - Basel: Birkhauser, Vol.OT18, pp.89-159.
  • Alpay D. and Dym H. (1993a): On a newclass of structured reproducing kernel spaces. - J. Funct.Anal., Vol.111, No.1, pp.1-28.
  • Alpay D. and Dym H. (1993b): On a newclass of reproducing kernel spaces and a new generalization of the Iohvidov laws. - Linear Algebra Appl., Vol.178, pp.109-183.
  • Alpay D. and Dym H. (1996): On a newclass of realization formulas and their application. - Linear Algebra Appl., Vol.241-243, pp.3-84.
  • Ball J.A. (1975): Models for noncontractions. - J. Math. Anal. Appl., Vol.52, No.2, pp.240-254.
  • de Branges L. (1963): Some Hilbert spaces of analytic functions I. - Trans. Amer. Math. Soc., Vol.106, pp.445-468.
  • Brodskii M.S. (1971): Triangular and Jordan Representations of Linear Operators. - Transl. Math. Monographs., Vol.32, Providence, RI: Amer. Math. Soc.
  • Dym H. (1989a): J Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation. - CBMS Reg. Conf., Ser. in Math., Vol.71, Providence, RI: Amer. Math. Soc.
  • Dym H. (1989b): On reproducing kernel spaces, J unitary matrixfunctions, interpolation and displacement rank, In: The Gohberg Anniversary Collection II (H. Dym, S. Goldberg, M.A. Kashoek and P. Lancaster, Eds.). - Oper. Theory Adv. Appl., Vol.OT41, Basel: Birkhauser, pp.173-239.
  • Dym H. (1994): Shifts, realizations and interpolation, redux, In: Operator Theory and its Applications (A. Feintuch and I. Gohberg, Eds.). - Oper. Theory Adv. Appl., Vol.OT73, Basel: Birkhauser, pp.182-243.
  • Dym H. (1998): A basic interpolation problem, In: Holomorphic Spaces, (S. Axler, J.E. Mc Carthy and D. Sarason, Eds.). -Cambridge: Cambridge University Press, pp.381-425.
  • Dym H. (2001): On Riccati equations and reproducing kernelspaces. - Oper. Theory Adv. Appl., to appear (alsoavailable at t http: www.wisdom.weizmann.ac.il).
  • Fuhrmann P.A. (1995): On the characterization and parametrization ofminimal spectral factors. - J. Math. Syst. Estim. Contr., Vol.5, No.4, pp.383-441.
  • Gombani A. and Weiland S. (2000): On the use of J-spectralfactorizations for dissipative dynamical systems. - Proc. 14-th Int. Conf. Math. Theory of Networks and Systems, MTNS, Perpignan, France, published on CD-ROM.
  • Karelin I., Lerer L. and Ran A.C.M. (2001): J-symmetric factorizations andalgebraic Riccati equations. - Oper. Theory Adv. Appl., (to appear).
  • Lerer L. and Ran A.C.M. (1997): J-pseudo-spectral and J-inner-pseudo-outerfactorizations for matrix polynomials. - Int. Eqns.Operat. Theory, Vol.29, pp.23-51.
  • Rovnyak J. (1968): Characterization of spaces K(M). - (unpublished manuscript).
  • Zhou K., Doyle J.C. and Glover K. (1996): Robust and Optimal Control. - New Jersey: Prentice Hall.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv11i1p35bwm
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