Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations
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- 作者：Christiane Tretter (1)
Christian Wyss (2) - 关键词：47A62 ; 47B44 ; 47N70 ; Riccati equation ; Hamiltonian ; dichotomous ; bisectorial ; invariant subspace ; p ; subordinate perturbation
- 刊名：Journal of Evolution Equations
- 出版年：2014
- 出版时间：March 2014
- 年：2014
- 卷：14
- 期：1
- 页码：121-153
- 全文大小：485 KB
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Christian Wyss (2)
1. Institute of Mathematics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
2. Department of Mathematics and Informatics, University of Wuppertal, Gau脽stra脽e 20, 42097, Wuppertal, Germany - ISSN：1424-3202
文摘
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.