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- W2085801480 abstract "Let L 0 be a closed densely defined symmetric semibounded operator with nonzero defect indices in a separable Hilbert space $mathcal H$ . It determines a Green system ${{mathcal H}, {mathcal B}; L_0, Gamma_1, Gamma_2}$ , where ${mathcal B}$ is a Hilbert space, and the $Gamma_i: {mathcal H} to mathcal B$ are operators connected by the Green formula $$ (L_0^*u, v)_{mathcal H}-(u,L_0^*v)_{mathcal H} =(Gamma_1 u, Gamma_2 v)_{mathcal B} - (Gamma_2 u, Gamma_1 v)_{mathcal B}. $$ The boundary space $mathcal B$ and the boundary operators Γ i are chosen canonically in the framework of the Vishik theory. With the Green system one associates a dynamical system with boundary control (DSBC): $$ begin{array}{lll} && u_{tt}+L_0^*u = 0, quad u(t) in {mathcal H}, quad t>0, && ubig|_{t=0}=u_tbig|_{t=0}=0, && Gamma_1 u = f, quad f(t) in {mathcal B},quad t geq 0. end{array} $$ We show that this system is controllable if and only if the operator L 0 is completely non-self-adjoint. A version of the notion of wave spectrum of L 0 is introduced. It is a topological space determined by L 0 and constructed from reachable sets of the DSBC. Bibliography: 15 titles." @default.
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- W2085801480 date "2013-09-05" @default.
- W2085801480 modified "2023-09-27" @default.
- W2085801480 title "Dynamical system with boundary control associated with a symmetric semibounded operator" @default.
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- W2085801480 doi "https://doi.org/10.1007/s10958-013-1501-8" @default.
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