Semiclassical Gevrey operators in the complex domain
Analysis of PDEs
2020-09-22 v1 Complex Variables
Abstract
We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the complexified phase space, which are extended almost holomorphically in the same Gevrey class, or in some larger space, to complex neighborhoods of these submanifolds. Using almost holomorphic extensions, we obtain uniformly bounded realizations of such operators on a natural scale of exponentially weighted spaces of holomorphic functions for all Gevrey indices, with remainders that are optimally small, provided that the Gevrey index is .
Cite
@article{arxiv.2009.09125,
title = {Semiclassical Gevrey operators in the complex domain},
author = {Michael Hitrik and Richard Lascar and Johannes Sjoestrand and Maher Zerzeri},
journal= {arXiv preprint arXiv:2009.09125},
year = {2020}
}