Volume growth, big jump, and essential spectrum for regular Dirichlet forms

2025/03/28 by Yuichi Shiozawa, Shiozawa, Yuichi
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2503.22899

openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an upper bound of the bottom of the essential spectrum for the generator associated with a regular Dirichlet form in terms of the rates of the volume growth/decay and big jump. Using this bound, we discuss how the bottom of the essential spectrum is affected by the volume growth and coefficient growth.

Related

• Growth and spectrum of diffusions
• The spectrum of the Laplacian and volume growth of proper minimal submanifolds
• Volume growth and spectrum for general graph Laplacians
• Type problem and the first eigenvalue
• Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals