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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hypoelliptic vector fields and continued fractions


Author: Stephen J. Greenfield
Journal: Proc. Amer. Math. Soc. 31 (1972), 115-118
MSC: Primary 43A85; Secondary 35H05, 46F99
DOI: https://doi.org/10.1090/S0002-9939-1972-0301459-3
MathSciNet review: 0301459
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Abstract: We consider global analytic hypoellipticity of constant coefficient differential operators on the $ 2$-torus, and prove that it is equivalent to a growth condition on the symbol. An example of a constant coefficient vector field which is globally analytic hypoelliptic but not globally hypoelliptic is constructed. Similar results are true on compact homogeneous spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0301459-3
Keywords: Fourier coefficients, continued fractions, global hypoellipticity
Article copyright: © Copyright 1972 American Mathematical Society