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

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

2010-04-26

arxiv.org/abs/1004.4396v1

Mathematics

Functional Analysis

20 pages

Scientific paper

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.

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