Hypoelliptic Vector Fields and Continued Fractions

1 January 1972

journal article
Published by JSTOR in Proceedings of the American Mathematical Society

Vol. 31 (1) , 115-118
https://doi.org/10.2307/2038524

Abstract

We consider global analytic hypoellipticity of constant coefficient differential operators on the -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.

Keywords

FOURIER COEFFICIENTS
CONTINUED FRACTIONS
GLOBAL HYPOELLIPTICITY

This publication has 3 references indexed in Scilit:

Global Hypoellipticity and Liouville Numbers
Proceedings of the American Mathematical Society, 1972
An Introduction to Number Theory.
The American Mathematical Monthly, 1971
An Introduction to Harmonic Analysis.
The American Mathematical Monthly, 1970