Invertible extensions of symmetric operators and the corresponding generalized resolvents

Abstract

In this paper we study invertible extensions of a symmetric operator in a Hilbert space $H$. All such extensions are characterized by a parameter in the generalized Neumann's formulas. Generalized resolvents, which are generated by the invertible extensions, are extracted by a boundary condition among all generalized resolvents in the Shtraus formula.

arXiv comment13 pages