I am quite new to dealing with operators with entries given by distributions and I would like to ask a few basic questions regarding their definitions. For simplicity let us assume that:
$A = \begin{pmatrix} \delta(t-t_{1}) & 0 \\ 0 & \delta(t-t_{2}) \end{pmatrix}$
where $t_{1}$ and $t_{2}$ are two real numbers.
- Is $A$ considered to be a self-adjoint? or what is it?
- Is $A$ considered to be bounded or unbounded (or maybe something else)?