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Pseudodifferential operators on non-quasianalytic classes of Beurling type

C. Fernández; A. Galbis; D. Jornet — 2005

Studia Mathematica

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 $_{(ω)}^{'}$ 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 $_{(ω)}^{'}$ . We also...

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