Nash-Moser theorem
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The Nash-Moser theorem, attributed to mathematicians John Forbes Nash and Jurgen Moser is a generalization of the inverse function theorem on Banach spaces to a class of 'tame' Frechet spaces. In contrast to the Banach space case, in which the invertibility of the derivative at a point is sufficient for a map to be locally invertible, the Nash-Moser theorem requires the derivative to be invertible in a neighbourhood. The theorem is widely used to prove local uniqueness for non-linear partial differential equations in spaces of smooth functions.
While Nash is credited with originating the theorem as a step in his proof of the Nash embedding theorem, Moser showed that Nash's methods could be successfully applied to solve problems on periodic orbits in celestial mechanics. A detailed exposition of the theorem and its applications was given by Hamilton (1982)
[edit] References
- R. HAMILTON "The inverse function theorem of Nash and Moser". Bulletin. of the Amer. Math. Soc., vol. 7, No 1 (1982) 65-222
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