Global regularity on $3$-dimensional solvmanifolds
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- by Jacek M. Cygan and Leonard F. Richardson PDF
- Trans. Amer. Math. Soc. 329 (1992), 473-488 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 473-488
- MSC: Primary 22E30; Secondary 35B65
- DOI: https://doi.org/10.1090/S0002-9947-1992-1055806-5
- MathSciNet review: 1055806