Date/heure
9 janvier 2020
14:15 - 15:15
Oratrice ou orateur
Clara Aldana
Catégorie d'évènement Séminaire Théorie de Lie, Géométrie et Analyse
Résumé
In this talk I will present the problem of finding extremal potentials for the functional determinant of a one-dimensional Schrödinger operator defined on a bounded interval with Dirichlet boundary conditions. We consider potentials in a fixed $L^q$ space with $qgeq 1$. Functional determinants of Sturm-Liouville operators with smooth potentials or with potentials with prescribed singularities have been widely studied, I will present a short review of these results and will explain how to extend the definition of the functional determinant to potentials in $L^q$. The maximization problem turns out to be equivalent to a problem in optimal control. I will explain how we obtain existence and uniqueness of the maximizers. The results presented in the talk are join work with J-B. Caillau (UCDA, CNRS, Inria, LJAD) and P. Freitas (Lisboa).