Pseudodifferential operators on non-quasianalytic classes of Beurling type
Volume 167 / 2005
Studia Mathematica 167 (2005), 99-131
MSC: 46F05, 47G30, 35S05, 46E10.
DOI: 10.4064/sm167-2-1
Abstract
We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class ${\mathcal D}'_{(\omega)}$ is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class ${\mathcal D}'_{(\omega)}$. We also develop the corresponding symbolic calculus.
