On a boundary pair of a dissipative operator

TL;DR

This paper shows that the boundary pair of a dissipative operator can be characterized by the unitary boundary pair of its symmetric component, providing insight into the structure of such operators.

Contribution

It establishes a link between dissipative operators and their symmetric parts through boundary pairs, offering a new perspective on their analysis.

Findings

Boundary pair of dissipative operator determined by symmetric part's boundary pair

Unitary boundary pair characterizes the dissipative operator's boundary conditions

Provides a theoretical framework connecting dissipative and symmetric operators

Abstract

The aim of this brief note is to demonstrate that the boundary pair of a dissipative operator is determined by the unitary boundary pair of its symmetric part.