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Canonical factorization and Riccati equations

  • Harm Bart
  • Marinus A. Kaashoek
  • André C. M. Ran
Part of the Operator Theory: Advances and Applications book series (OT, volume 200)

Abstract

In this chapter the canonical factorization theorem from Section 7.1 is presented in a different way using the notion of an angular subspace and Riccati equations. In this case one has to look for solutions of the Riccati equation that have additional spectral properties. Section 12.1, which has a preliminary character, deals with angular subspaces, and in particular those that are also spectral subspaces. Section 12.2 deals with the connection between factorization and Riccati equations in general, while Section 12.3 contains the main result. It specifies further the main theorem of the second section for the case of canonical factorization. In Section 12.4, as an application, we solve in state space form the problem of obtaining a right canonical factorization when a left one is given (or reversely).

Keywords

Riccati Equation Product Rule Exterior Domain Riemann Sphere Invertible Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser/Springer Basel AG 2010

Authors and Affiliations

  • Harm Bart
    • 1
  • Marinus A. Kaashoek
    • 2
  • André C. M. Ran
    • 2
  1. 1.Econometrisch InstituutErasumus Universiteit RotterdamRotterdamThe Netherlands
  2. 2.Department of Mathematics, FEWVrije UniversiteitAmsterdamThe Netherlands

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