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

A. V. Strauss

Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 179-208.

Résumé

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 $\operatorname{Im}\lambda0$. The set of all generalized resolvents of the operator $A$ is characterized.

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