Solvable Extensions of Some Nondensely Defined Operators and the Resolvents of These Extensions

Abstract

In terms of abstract boundary conditions, we study a class of extensions of finite-dimensional restrictions of closed densely defined linear operators acting in Hilbert spaces. By the methods of the theory of linear relations, we find the resolvent sets and construct the resolvents of the analyzed extensions. The set of these extensions is parameterized by a certain auxiliary operator. In the case where this operator is normally solvable, we present certain improvements of the basic results.