We consider the following objects: ${cal S}$ is a closed subspace of a Hilbert Space ${cal H}$, ${cal P}$ is the projection operator for ${cal S}$, and ${cal U}(t)$ is a strongly continuous group of unitary operators on ${cal H}$ with infinitesimal generator ${cal A}$. We let $U={cal U}(T)$, where $T>0$ is fixed. The questions that we ask are begin{itemize} item Under what conditions is $mathcal{P}Umathcal{P}$ a contraction? item Under what conditions can we steer $g in mathcal{S}$ to $hin mathcal{S}$ in the sense that we can find $fin mathcal{H}$ such that ${cal P}f=g$ and ${cal P}Uf=h$? end{itemize} |
Keywords
control, Hilbert space, over-determined
Math Review Classification
Primary 47A50, 93C20
; Secondary 35N10, 35N05
Last Updated
17 May 1999
Length
6 pages
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