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- W2065280524 abstract "We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schrödinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions." @default.
- W2065280524 created "2016-06-24" @default.
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- W2065280524 date "2011-09-15" @default.
- W2065280524 modified "2023-10-14" @default.
- W2065280524 title "Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces" @default.
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- W2065280524 doi "https://doi.org/10.1215/00127094-1433403" @default.
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