Global regularity on 3-Dimensional solvmanifolds
Let M be any 3-dimensional (nonabelian) compact solvmanifold.We apply the methods of representation theory to study the convergence of Fourier series of smooth global solutions to first order invariant partial differential equations Df = g in C∞(M). We show that 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. © 1992 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Cygan, J., & Richardson, L. (1992). Global regularity on 3-Dimensional solvmanifolds. Transactions of the American Mathematical Society, 329 (2), 473-488. https://doi.org/10.1090/S0002-9947-1992-1055806-5