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GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS
Published online by Cambridge University Press: 05 January 2024
Abstract
We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on $T \times G$, where T is a compact Riemannian manifold and G is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on G and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.
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- © The Author(s), 2024. Published by Cambridge University Press
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