M-Accretive Realisations of Skew-Symmetric Operators

TL;DR

This paper characterizes all m-accretive restrictions of skew-symmetric operators on Hilbert spaces using deficiency spaces, with applications to PDEs and boundary conditions, advancing the understanding of operator restrictions.

Contribution

It provides a complete characterization of m-accretive restrictions of skew-symmetric operators via deficiency spaces, including practical examples and PDE applications.

Findings

Characterization of m-accretive restrictions using deficiency spaces

Application to PDEs with impedance boundary conditions

Illustrative examples demonstrating the theory

Abstract

We consider skew-symmetric operators $A_{0}$ on a Hilbert space $H$ and characterise all (nonlinear) m-accretive restrictions of $A:=-A_{0}^{\ast}$ in terms of the "deficiency spaces" $\ker(1\pm A)$. The results are illustrated by several examples and applied to a partial differential equation with an impedance type boundary condition.