Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms

TL;DR

This paper explores the spectral theory of strongly local Dirichlet forms, focusing on generalized eigenfunctions and their relation to spectral properties, supported by various examples.

Contribution

It introduces the connection between generalized eigenfunctions and spectral properties in the context of strongly local Dirichlet forms, with illustrative applications.

Findings

Established links between eigenfunctions and spectral characteristics.

Provided examples demonstrating the theory's applicability.

Enhanced understanding of spectral analysis in Dirichlet form frameworks.

Abstract

We present an introduction to the framework of strongly local Dirichlet forms and discuss connections between the existence of certain generalized eigenfunctions and spectral properties within this framework. The range of applications is illustrated by a list of examples.