D-harmonic distributions and global hypoellipticity on nilmanifolds
Let M = Γ\N be a compact nilmanifold. A system of differential operators D1, …, Dk on M is globally hypoelliptic (GH) if when D1f = g1,…, Dkf=gk with f ∈ D’ (M), g1, …, gk ∈ C∞ (M) then f ∈ C∞ (M). Let X1, …, Xk be real vector fields on M induced by the Lie algebra N of N. We study the relationships between (GH) of the system X1, …, Xk on M, (GH) of the operator D = X12 + … + Xk2, the constancy of D-harmonic distributions on M, and related algebraic conditions on X1, …, Xk ∈ N. © 1991 by Pacific Journal of Mathematics.
Publication Source (Journal or Book title)
Pacific Journal of Mathematics
Cygan, J., & Richardson, L. (1991). D-harmonic distributions and global hypoellipticity on nilmanifolds. Pacific Journal of Mathematics, 147 (1), 29-46. https://doi.org/10.2140/pjm.1991.147.29