Geometric Microlocal Analysis in Denjoy-Carleman classes
Abstract
A systematic geometric theory for the ultradifferentiable (non-quasianalytic and quasianalytic) wavefront set similar to the well-known theory in the classic smooth and analytic setting is developed. In particular an analogue of Bony's Theorem and the invariance of the ultradifferentiable wavefront set under diffeomorphisms of the same regularity is proven using a Theorem of Dyn'kin about the almost-analytic extension of ultradifferentiable functions. Furthermore we prove a microlocal elliptic regularity theorem for operators defined on ultradifferentiable vector bundles. As an application we show that Holmgren's theorem and several generalizations hold for operators with quasianalytic coefficients.
Keywords
Cite
@article{arxiv.1805.11320,
title = {Geometric Microlocal Analysis in Denjoy-Carleman classes},
author = {Stefan Fürdös},
journal= {arXiv preprint arXiv:1805.11320},
year = {2020}
}
Comments
Section 6 was revised, in particular in Theorem 6.1 an additional condition on the weight sequence has to be assumed and its proof was adapted; several typos were fixed throughout the paper