Hypoellipticity of analytic differential operators in general ultradifferentiable classes

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.