Abstract

We show global normal forms of first order real principal type C∞ and Gevrey pseudodifferential operators on the torus T2 under generalized small divisor conditions on the principal symbol. We introduce a family of logarithmic Hausdorff dimensions associated to the Gevrey classes in order to examine the corresponding exceptional sets. We study the global hypoellipticity of such operators through inhomogenous Diophantine conditions for the normal forms.

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