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## Growth of Sobolev norms for abstract linear Schrödinger Equations

• Date November 9, 2017
• Hour 3 pm
• Room GSSI Main Lecture Hall
• Speaker Alberto Maspero (SISSA)
• Area Maths

ABSTRACT

We prove an abstract theorem giving a epsilon bound for any  $\dpi{300}\inline t^\epsilon$ bound for any $\dpi{300}\inline \epsilon> 0$ on the growth of the Sobolev norms in some abstract linear time dependent Schrödinger equations.
The abstract theorem is applied to several cases, including perturbations of (i) Schrödinger equation on a Zoll manifold; (ii) resonant or nonresonant Harmonic oscillators in R^d.
The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. This is a joint work with D. Bambusi, B. Grebert and D. Robert.