Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms

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.

References in corpus (5)

• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
• PT-symmetric quantum mechanics
• Lower bounds on the lowest spectral gap of singular potential Hamiltonians
• Eigenfunction expansion for Schrodinger operators on metric graphs
• An Estimate of the Gap of the First Two Eigenvalues in the Schrödinger Operator

Cited by in corpus (3)

• Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials
• Essential self-adjointness, generalized eigenforms, and spectra for the $\bar{\partial }$-Neumann problem on $G$-manifolds
• Powers Of Generators On Dirichlet Spaces And Applications To Harnack Principles