A conic manifold perspective of elliptic operators on graphs

TL;DR

This paper provides a clear condition for the existence of a sector of minimal growth for certain elliptic operators on graphs, focusing on Coulomb-type singular potentials using cone operator theory.

Contribution

It introduces a simple, explicit criterion for minimal growth sectors of elliptic operators on graphs with Coulomb singularities, based on cone operator theory.

Findings

Established a sufficient condition for minimal growth sectors.

Analyzed elliptic operators with Coulomb-type singular potentials.

Applied cone operator theory to graph-based differential operators.

Abstract

We give a simple, explicit, sufficient condition for the existence of a sector of minimal growth for second order regular singular differential operators on graphs. We specifically consider operators with a singular potential of Coulomb type and base our analysis on the theory of elliptic cone operators.