Growth and spectrum of diffusions
Lino Notarantonio
TL;DR
This paper establishes an upper bound on the essential spectrum's lower end for diffusions, linking it to the volume growth of the space, extending Brooks' earlier results.
Contribution
It generalizes Brooks' result by providing a new bound on the spectrum of diffusions based on volume growth.
Findings
Upper bound on the essential spectrum derived
Relation between spectrum and volume growth established
Generalization of Brooks' theorem achieved
Abstract
We prove an upper bound on the bottom of the essential spectrum of a diffusion in term of the growth of the volume of , generalizing a result by R. Brooks.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · Nonlinear Partial Differential Equations