Contraction semigroups of elliptic quadratic differential operators
Analysis of PDEs
2007-05-23 v1
Abstract
We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We establish in this paper that under the assumption of ellipticity, as soon as the real part of their Weyl symbols is a non-zero non-positive quadratic form, the norm of contraction semigroups generated by these operators decays exponentially in time.
Cite
@article{arxiv.0705.0950,
title = {Contraction semigroups of elliptic quadratic differential operators},
author = {Karel Pravda-Starov},
journal= {arXiv preprint arXiv:0705.0950},
year = {2007}
}