Global Regularity on 3-dimensional Solvmanifolds
نویسندگان
چکیده
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.
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تاریخ انتشار 2010