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- W2952544271 abstract "Given, on the Hilbert space $H_0$, the self-adjoint operator $B$ and the skew-adjoint operators $C_1$ and $C_2$, we consider, on the Hilbert space $Hsimeq D(B)oplusH_0$, the skew-adjoint operator $$W=[begin{matrix} C_2&uno -B^2&C_1end{matrix}]$$ corresponding to the abstract wave equation $ddotphi-(C_1+C_2)dotphi=-(B^2+C_1C_2)phi$. Given then an auxiliary Hilbert space $fh$ and a linear map $tau:D(B^2)tofh$ with a kernel $K$ dense in $H_0$, we explicitly construct skew-adjoint operators $W_Theta$ on a Hilbert space $H_Thetasimeq D(B)oplusH_0oplus fh$ which coincide with $W$ on $NsimeqKoplus D(B)$. The extension parameter $Theta$ ranges over the set of positive, bounded and injective self-adjoint operators on $fh$. In the case $C_1=C_2=0$ our construction allows a natural definition of negative (strongly) singular perturbations $A_Theta$ of $A:=-B^2$ such that the diagram $$ begin{CD} W @>>> W_Theta @AAA @VVV A@>>> A_Theta end{CD} $$ is commutative." @default.
- W2952544271 created "2019-06-27" @default.
- W2952544271 creator A5034542231 @default.
- W2952544271 date "2004-03-23" @default.
- W2952544271 modified "2023-09-27" @default.
- W2952544271 title "Singular Perturbations of Abstract Wave equations" @default.
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