Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

Abstract

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.

20 pages

References in corpus (2)

• Sharp Garding inequality on compact Lie groups
• On multipliers on compact Lie groups

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