  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
$\H\simeq D(B)\oplus\H_0$, the skew-adjoint operator $$W=[\begin{matrix}
C_2&\uno -B^2&C_1\end{matrix}]$$ corresponding to the abstract wave equation
$\ddot\phi-(C_1+C_2)\dot\phi=-(B^2+C_1C_2)\phi$. Given then an auxiliary
Hilbert space $\fh$ and a linear map $\tau:D(B^2)\to\fh$ with a kernel $\K$
dense in $\H_0$, we explicitly construct skew-adjoint operators $W_\Theta$ on a
Hilbert space $\H_\Theta\simeq D(B)\oplus\H_0\oplus \fh$ which coincide with
$W$ on $\N\simeq\K\oplus D(B)$. 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.
