Schrödinger evolution of superoscillations under different potentials

Superoscillations appear in several branches of science and technology and in particular they are the outcome of weak measurements. So it important to study the evolution of superoscillatory functions as initial data for the Schrödinger equation when the Hamiltonian operator contains different potentials. Since the most important functions appearing in weak measurements are not squared integrable it is necessary to study the evolution problem using techniques that use convolution operators acting on spaces of entire functions. In this paper we give an introduction to this technique and we give the state of the art for this investigation together with some new results, in which we consider time dependent Hamiltonians.