期刊
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
卷 20, 期 3, 页码 476-499出版社
SPRINGER BIRKHAUSER
DOI: 10.1007/s00041-014-9322-9
关键词
Pseudo-differential operators; compact Lie groups; microlocal analysis; elliptic operators; global hypoellipticity; Leibniz formula
资金
- EPSRC [EP/G007233/1, EP/E062873/1]
- EPSRC [EP/G007233/1, EP/E062873/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E062873/1, EP/G007233/1] Funding Source: researchfish
In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. 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, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.
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