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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Springer Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-013-0210-6
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Journal of Evolution Equations – Springer Journals
Published: Mar 1, 2014