Compactness Criteria for the Resolvent of the Fokker-Planck operator

TL;DR

This paper establishes new criteria for the compactness of the resolvent of a Fokker-Planck operator with potential, based on the eigenvalues of the Hessian matrix, advancing spectral analysis methods.

Contribution

It introduces novel compactness criteria for the resolvent of the Fokker-Planck operator using a multiplier method related to the Hessian eigenvalues.

Findings

New compactness criteria involving Hessian eigenvalues

Spectral properties of Fokker-Planck operators analyzed

Multiplier method inspired by Nicolas Lerner used

Abstract

In this paper we study the spectral property of a Fokker-Planck operator with potential. By virtue of a multiplier method inspired by Nicolas Lerner, we obtain new compactness criteria for its resolvent, involving the control of the positive eigenvalues of the Hessian matrix of the potential.