Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

Abstract

We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasianalytic Gelfand-Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pull-backs and products. We further study quasianalytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.

26 pages

References in corpus (3)

• The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions
• The Gabor wave front set
• Exponentially sparse representations of Fourier integral operators

Cited by in corpus (2)

• A smooth introduction to the wavefront set
• On the Schrödinger equation with potential in modulation spaces