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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 two-step compact nilmanifolds


Authors: Jacek M. Cygan and Leonard F. Richardson
Journal: Trans. Amer. Math. Soc. 279 (1983), 537-554
MSC: Primary 22E27; Secondary 22E30, 35A99
MathSciNet review: 709567
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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 two-step compact nilmanifold. 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 multidimensional tori.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0709567-1
PII: S 0002-9947(1983)0709567-1
Article copyright: © Copyright 1983 American Mathematical Society