EXTENSIONS AND GENERALIZED RESOLVENTS OF A SYMMETRIC OPERATOR WHICH IS NOT DENSELY DEFINED

Abstract

We consider extensions of a closed symmetric operator whose domain is, in general, not dense in the given Hilbert space . In particular, we study self-adjoint extensions outside and the one-parameter families of operators () generated by them in which are dissipative for . The set of all generalized resolvents of the operator is characterized.