Remarks on Analytic Hypoellipticity

Abstract

We will compare the foIlowing ideas: analytic hypoeIlipticity on open subsets of Euclidean space; global analytic hypoeIlipticity; analytic hypoeIlipticity in the sense of germs. We present a new operator which posseses Treves curves, yet is analytic hypoelliptic in the sense of germs. That is, the analog of the Treves conjecture, in the sense of germs, is false.