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arXiv · 1707.01668

Tame majorant analyticity for the Birkhoff map of the defocusing Nonlinear Schr\"odinger equation on the circle

Alberto Maspero
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Abstract

For the defocusing Nonlinear Schr\"odinger equation on the circle, we construct a Birkhoff map $\Phi$ 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 $\Phi$ 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 $\Phi$ fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem, which is an infinite dimensional Vey type theorem.

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Alberto Maspero. 2017-07-06. Tame majorant analyticity for the Birkhoff map of the defocusing Nonlinear Schr\"odinger equation on the circle. https://doi.org/10.1088/1361-6544/aaa7ba

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