Generalized resolvents of symmetric and isometric operators: the Shtraus approach

Abstract

This exposition paper is devoted to the theory of Abram Vilgelmovich Shtraus and his disciples and followers. This theory studies the so-called generalized resolvents of symmetric and isometric operators in a Hilbert space and provides alternative formulas to the well-known Krein-type formulas. We think that it would be convenient to have an exposition of the corresponding theory with full proofs and necessary corrections.