Hypoelliptic vector fields and continued fractions
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- by Stephen J. Greenfield
- Proc. Amer. Math. Soc. 31 (1972), 115-118
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301459-3
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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.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
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
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- Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Pure and Applied Mathematics, No. 19, Marcel Dekker, Inc., New York, 1973. MR 0498996
Bibliographic 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