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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 regularity on $ 3$-dimensional solvmanifolds


Authors: Jacek M. Cygan and Leonard F. Richardson
Journal: Trans. Amer. Math. Soc. 329 (1992), 473-488
MSC: Primary 22E30; Secondary 35B65
MathSciNet review: 1055806
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Abstract: 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^\infty }(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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1055806-5
PII: S 0002-9947(1992)1055806-5
Article copyright: © Copyright 1992 American Mathematical Society