For the defocusing nonlinear Schrö dinger equation on the circle, we construct a Birkhoff map Φ which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of Φ by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of Φ fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1-24), which is an infinite dimensional Vey type theorem.

Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle / Maspero, A.. - In: NONLINEARITY. - ISSN 0951-7715. - 31:5(2018), pp. 1981-2030. [10.1088/1361-6544/aaa7ba]

Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle

Maspero, A.
2018

Abstract

For the defocusing nonlinear Schrö dinger equation on the circle, we construct a Birkhoff map Φ which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of Φ by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of Φ fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1-24), which is an infinite dimensional Vey type theorem.
31
5
1981
2030
https://arxiv.org/abs/1707.01668
Maspero, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/77238
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