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The Morse lemma for Banach spaces
1969
Bulletin of the American Mathematical Society
Preserved Fulltext
THEOREM. Let V be a Banach space, O a convex neighborhood of the origin in V and f: Q-*R a C k+2 f unction (feèl) having the origin as a nondegenerate critical point, with ƒ (0) = 0. Then there is a neighborhood U of the origin and a C k diffeomorphism : U-+6 with cf>(0) = 0 and (Z>0)o = the identity map of V such that for x£ Uf((x)) = i(D 2 f)o(x, x).
doi:10.1090/s0002-9904-1969-12318-9
fatcat:qk3pclh5tbcsdjmiiazulqxxzu