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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.


References [Enhancements On Off] (What's this?)

  • [G] Stephen J. Greenfield and Nolan R. Wallach, Global hypoellipticity and Liouville numbers, Proc. Amer. Math. Soc. 31 (1972), 112-114. MR 0296508 (45:5568)
  • [H] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford Univ. Press, London, 1954. MR 16, 673. MR 0067125 (16:673c)
  • [K] Y. Katznelson, An introduction to harmonic analysis, Wiley, New York, 1968. MR 40 #1734. MR 0248482 (40:1734)
  • [S] H. M. Stark, An introduction to number theory, Markham, Chicago, Ill., 1970. MR 40 #7186. MR 0253973 (40:7186)
  • [W] Nolan R. Wallach, Differential operators on homogeneous spaces, Marcel Dekker, New York (to appear). MR 0498996 (58:16978)

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Additional Information

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

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