Global Hypoellipticity and Liouville Numbers

1 January 1972

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

Vol. 31 (1) , 112-114
https://doi.org/10.2307/2038523

Abstract

We consider global hypoellipticity of constant coefficient differential operators on the -torus, and prove that it is equivalent to an algebraic growth condition on the symbol. This is applied to give necessary and sufficient conditions that a constant coefficient vector field be globally hypoelliptic. Similar results are true on compact homogeneous spaces.

Keywords

FOURIER COEFFICIENTS
LIOUVILLE NUMBERS
GLOBAL HYPOELLIPTICITY

This publication has 1 reference indexed in Scilit:

Functions Which are Divergences
American Journal of Mathematics, 1970