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

Yuichi Shiozawa

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arXiv · 2503.22899

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

Yuichi Shiozawa

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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.

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Yuichi Shiozawa. 2025-03-28. Volume growth, big jump, and essential spectrum for regular Dirichlet forms. https://arxiv.org/abs/2503.22899

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