Maximal-quasi-accretive Laplacians on finite metric graphs

TL;DR

This paper characterizes boundary conditions on finite metric graphs that produce quasi-m-accretive and m-accretive Laplacian operators, expanding understanding of their spectral properties and operator theory.

Contribution

It provides a complete characterization of boundary conditions leading to quasi-m-accretive and m-accretive Laplacians on finite metric graphs.

Findings

Complete classification of boundary conditions for quasi-m-accretive Laplacians.

Identification of conditions for m-accretive operators.

Extension of spectral theory for differential operators on graphs.

Abstract

For a finite not necessarily compact metric graph, one considers the differential expression $-\frac{d^2}{d x^2}$ on each edge. The boundary conditions at the vertices of the graph yielding quasi-m-accretive as well as m-accretive operators are completely characterized.