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

• P. Gérard ^[1] ; T. Kappeler ^[2] ; P. Topalov ^[3]
  1. [1] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
  2. [2] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  3. [3] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01053-6
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• Resumen

  • 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).

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