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Global solvability and hypoellipticity on compact manifolds

Abstract

We shall study the problems of global hypoellipticity and global solvability of operators defined on $G$-principle bundles $\Omega$, where $G$ is a compact Lie group that acts on a compact manifold $M$. We are particularly interested in cases where the $G$-principal bundle is the canonical product $\Omega = M\times \TT^m$ and where the operators are associated with differential complexes arising from locally integrable structures of tube type. We also study scalar operators given by sum of squares of vector fields when $M=\TT^n$. (AU)

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