Maximal determinants of Schrödinger operators on bounded intervals (Q2208624)

From the authors' abstract: ``We consider 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 under an \(L^q\)-norm restriction (\(q \ge 1\)). This is done by first extending the definition of the functional determinant to the case of \(L^q\) potentials and showing the resulting problem to be equivalent to a problem in optimal control, which we believe to be of independent interest.'' The proofs of existence and uniqueness of the solution are developed separately for the cases \(q=1\) and \(q>2\). A complete characterization and some special properties of the solutions are established for the cases \(q=1\) and \(q=2\), which are relevant special cases both from a mathematical point of view and for applications in Physics.