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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global hypoellipticity and Liouville numbers


Authors: Stephen J. Greenfield and Nolan R. Wallach
Journal: Proc. Amer. Math. Soc. 31 (1972), 112-114
MSC: Primary 34H05; Secondary 47F05
MathSciNet review: 0296508
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Abstract: We consider global hypoellipticity of constant coefficient differential operators on the $ 2$-torus, and prove that it is equivalent to an algebraic growth condition on the symbol. This is applied to give necessary and sufficient conditions that a constant coefficient vector field be globally hypoelliptic. Similar results are true on compact homogeneous spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296508-5
PII: S 0002-9939(1972)0296508-5
Keywords: Fourier coefficients, Liouville numbers, global hypoellipticity
Article copyright: © Copyright 1972 American Mathematical Society