Ultradifferentiable CR Manifolds

Fürdös, Stefan

doi:10.1007/s12220-019-00191-6

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Invariance Of the Wavefront Set Under Ultradifferentiable Ma...1

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2020

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Cited by 2 publications

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“…without parameters), we have decided to include the general statement because we think it is of independent interest. We also have an application for the parameter version of the theorem in our upcoming paper [27].…”

Section: Invariance Of the Wavefront Set Under Ultradifferentiable Ma...mentioning

confidence: 99%

Geometric Microlocal Analysis in Denjoy-Carleman classes

Fürdös

2018

Preprint

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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.

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Section: Invariance Of the Wavefront Set Under Ultradifferentiable Ma...mentioning

confidence: 99%