Sch'nol's Theorem For Strongly Local Forms

TL;DR

This paper extends Sch'nol's theorem to strongly local Dirichlet forms with measure perturbations, providing insights into quantum graphs with specific boundary conditions.

Contribution

It introduces a generalized version of Sch'nol's theorem applicable to strongly local forms perturbed by measures, including quantum graph applications.

Findings

Established a variant of Sch'nol's theorem for strongly local Dirichlet forms.

Applied the theorem to quantum graphs with delta and Kirchhoff boundary conditions.

Enhanced understanding of spectral properties in perturbed local forms.

Abstract

We prove a variant of Sch'nol's theorem in a general setting: for generators of strongly local Dirichlet forms perturbed by measures. As an application, we discuss quantum graphs with $\delta$- or Kirchhoff boundary conditions.