analysis of partial differential equations

Hypoellipticity of analytic differential operators in general ultradifferentiable classes

arXiv:2511.13579 · doi:10.1007/s11868-026-00803-0

summary

The paper proves that analytic pseudodifferential and Fourier integral operators act nicely on ultradifferentiable function spaces and uses this to extend Treves' hypoellipticity results for analytic operators of principal type to ultradifferentiable settings.

Abstract

We show that analytic pseudodifferential and Fourier integral operators behave well for ultradifferentiable classes satisfying minimal regularity properties. As an application we investigate the ultradifferentiable regularity properties of several examples of analytic differential operators. In particular we extend Treves' characterization of the hypoellipticity of analytic operators of principal type to the ultradifferentiable category.

Corrected version to be published in J. Pseudo-Differ. Oper. Appl

Topics & keywords

#hypoellipticity#ultradifferentiable classes#analytic pseudodifferential operators#Fourier integral operators#principal type operatorsultradifferentiable regularityanalytic differential operatorsTreves' characterizationpseudodifferential operatorsFourier integral operators
Hypoellipticity of analytic differential operators in general ultradifferentiable classes · wovepaper