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Dichotomy properties of Hamiltonians for linear systems in extrapolation spaces
Author(s) -
Wyss Christian
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610432
Subject(s) - linear subspace , extrapolation , mathematics , invariant (physics) , riccati equation , hamiltonian (control theory) , operator (biology) , linear system , pure mathematics , mathematical analysis , mathematical physics , partial differential equation , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
Abstract For the Hamiltonian operator matrix from systems theory the existence of invariant subspaces corresponding to the spectrum in the right and left half‐plane is shown. The control and observation operators are unbounded in the sense that they map into extrapolation spaces, thereby allowing for PDE systems with control and observation on the boundary. The invariant subspaces are then used to construct solutions of the corresponding Riccati equation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)