Extensions and generalized resolvents of a symmetric operator which is not densely defined

We consider extensions of a closed symmetric operator $A$ whose domain is, in general, not dense in the given Hilbert space $H$. In particular, we study self-adjoint extensions outside $H$ and the one-parameter families of operators $B_\lambda\supset A$ ($\operatorname{Im}\lambda\ne0$) generated by them in $H$ which are dissipative for $\operatorname{Im}\lambda<0$. The set of all generalized resolvents of the operator $A$ is characterized.