English

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

Probability 2025-04-01 v1 Functional Analysis

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.

Keywords

Cite

@article{arxiv.2503.22899,
  title  = {Volume growth, big jump, and essential spectrum for regular Dirichlet forms},
  author = {Yuichi Shiozawa},
  journal= {arXiv preprint arXiv:2503.22899},
  year   = {2025}
}
R2 v1 2026-06-28T22:38:42.985Z