Global solvability on two-step compact nilmanifolds
We apply the methods of representation theory of nilpotent Lie groups to study the convergence of Fourier series of smooth global solutions to first order invariant partial differential equations D = g in C∞ of a two-step compact nilmani- fold. We show that, under algebraically well-defined conditions on D in the complexified Lie algebra, smooth infinite-dimensional irreducible solutions, when they exist, satisfy estimates strong enough to guarantee uniform convergence of the irreducible (or primary) Fourier series to a smooth global solution. Such strong estimates are not possible on multidimensionaltori. © 1983 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Cygan, J., & Richardson, L. (1983). Global solvability on two-step compact nilmanifolds. Transactions of the American Mathematical Society, 279 (2), 537-554. https://doi.org/10.1090/S0002-9947-1983-0709567-1