Resumen de On the analyticity of the nonlinear Fourier transform of the Benjamin-Ono equation on T

P. Gérard, Thomas Kappeler, P. Topalov

• We prove that the nonlinear Fourier transform of the Benjamin-Ono equation on T, also referred to as Birkhoff map, is a real analytic diffeomorphism from the scale of Sobolev spaces Hs 0 (T, R), s > −1/2, to the scale of weighted 2−sequence spaces, h s+1/2 r,0 (N, C), s > −1/2. As an application we show that for any −1/2 < s < 0, the flow map of the Benjamin-Ono equation St 0 : Hs 0 (T, R) → Hs 0 (T, R) is nowhere locally uniformly continuous in Hs 0 (T, R).