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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Global solvability on compact nilmanifolds of three or more steps


Authors: Jacek M. Cygan and Leonard F. Richardson
Journal: Trans. Amer. Math. Soc. 301 (1987), 343-373
MSC: Primary 22E27; Secondary 22E30, 58G25
MathSciNet review: 879578
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Abstract: 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 $ Df = g$ in $ {C^\infty}$ of a compact nilmanifold of three or more steps. We investigate which algebraically well-defined conditions on $ D$ in the complexified Lie algebra imply 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. This extends and improves the results of an earlier two step paper.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0879578-8
PII: S 0002-9947(1987)0879578-8
Article copyright: © Copyright 1987 American Mathematical Society