Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics
Analysis of PDEs
2009-02-23 v1 Spectral Theory
Abstract
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we establish semiclassical hypoelliptic a priori estimates with a loss of the full power of the semiclassical parameter, giving a localization for the low lying spectral values of the operator.
Keywords
Cite
@article{arxiv.0902.3491,
title = {Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics},
author = {Michael Hitrik and Karel Pravda-Starov},
journal= {arXiv preprint arXiv:0902.3491},
year = {2009}
}