Global Hypoellipticity for Strongly Invariant Operators

Abstract

In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator $P$ with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that $P$ is globally hypoelliptic. We also investigate relations between the global hypoellipticity of $P$ and global subelliptic estimates.

arXiv comment20 pages

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Cited by in corpus (2)

• Global hypoellipticity and global solvability for vector fields on compact Lie groups
• Global solutions for systems of strongly invariant operators on closed manifolds