Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

Tretter, Christiane; Wyss, Christian (2014). Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations. Journal of evolution equations, 14(1), pp. 121-153. Birkhäuser 10.1007/s00028-013-0210-6

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An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Tretter, Christiane and Wyss, Christian

Subjects:

500 Science > 510 Mathematics

ISSN:

1424-3199

Publisher:

Birkhäuser

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:41

Last Modified:

07 Oct 2015 10:24

Publisher DOI:

10.1007/s00028-013-0210-6

BORIS DOI:

10.7892/boris.66709

URI:

https://boris.unibe.ch/id/eprint/66709

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