Dissipative extension theory for linear relations

TL;DR

This paper develops a comprehensive theory for dissipative extensions of linear relations, generalizing symmetric extension theory and analyzing spectral properties of these extensions.

Contribution

It introduces a unified framework for dissipative extension theory of linear relations, extending classical symmetric operator results to a broader context.

Findings

Proves properties of dissipative relations.

Provides spectral analysis of dissipative extensions.

Generalizes symmetric extension theory to linear relations.

Abstract

This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the properties of dissipative relations are proven. Finally, we deal with the spectral properties of dissipative extensions of dissipative relations and provide results concerning particular realizations of this general setting.