Maximal determinants of Schrödinger operators on bounded intervals
Résumé
We consider the problem of finding extremal potentials for the functional determinant of a one-dimensional Schro ̈dinger operator defined on a bounded interval with Dirichlet boundary conditions under an Lq-norm res- triction (q ≥ 1). This is done by first extending the definition of the functional determinant to the case of Lq potentials and showing the resulting problem to be equivalent to a problem in optimal control, which we believe to be of independent interest. We prove existence, uniqueness and describe some basic properties of solutions to this problem for all q ≥ 1, providing a complete characterization of extremal potentials in the case where q is one (a pulse) and two (Weierstrass’s ℘ function).
Domaines
Optimisation et contrôle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
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