Year: 2020
Type: article
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.
Source: Pacific Journal of Mathematics
Author: Stefan Fürdös
Institution: University of Vienna
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2807420542