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

Abstract

For the defocusing Nonlinear Schrödinger 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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References in corpus (3)

• On time dependent Schr{ö}dinger equations: global well-posedness and growth of Sobolev norms
• Reducibility of the Quantum Harmonic Oscillator in $d$-dimensions with Polynomial Time Dependent Perturbation
• On the growth of Sobolev norms for NLS on $2d$ and $3d$ manifolds

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