Spaces of Boundary Values and Dissipative Extensions of Symmetric Relations

Abstract

For a closed symmetric linear relation L 0 with an arbitrary index of the defect, we introduce the notion of boundary quadruplet, with the help of which we deduce an abstract analog of the formula of integration by parts and prove its existence. In the case where this relation has equal defect numbers, we establish the relationship between the introduced object and the known notion of boundary triplet. In terms of boundary quadruplets, we present a description of maximally dissipative and maximally accumulative extensions of the relation L 0.