Hypoelliptic vector fields and continued fractions
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- by Stephen J. Greenfield PDF
- Proc. Amer. Math. Soc. 31 (1972), 115-118 Request permission
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.References
- Stephen J. Greenfield and Nolan R. Wallach, Global hypoellipticity and Liouville numbers, Proc. Amer. Math. Soc. 31 (1972), 112–114. MR 296508, DOI 10.1090/S0002-9939-1972-0296508-5
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Additional Information
- © Copyright 1972 American Mathematical Society
- 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