Compactness of the resolvent for the Witten Laplacian
Analysis of PDEs
2018-04-04 v2 Spectral Theory
Abstract
In this paper we consider the Witten Laplacian on 0-forms and give sufficient conditions under which the Witten Laplacian admits a compact resolvent. These conditions are imposed on the potential itself, involving the control of high order derivatives by lower ones, as well as the control of the positive eigenvalues of the Hessian matrix. This compactness criterion for resolvent is inspired by the one for the Fokker-Planck operator. Our method relies on the nilpotent group techniques developed by Helffer-Nourrigat [Hypoellipticit\'e maximale pour des op\'erateurs polyn\^omes de champs de vecteurs, 1985].
Keywords
Cite
@article{arxiv.1707.04745,
title = {Compactness of the resolvent for the Witten Laplacian},
author = {Wei-Xi Li},
journal= {arXiv preprint arXiv:1707.04745},
year = {2018}
}
Comments
25pages