Superoscillating sequences as solutions of generalized Schrödinger equations

Weak measurement and weak values have a very deep meaning in quantum mechanics, and new phenomena associated to them have recently been observed experimentally. These measurements give rise to the notion of superoscillating sequences of functions. In the recent years the authors have started an intensive study of this topic from the mathematical point of view. In this paper we use a generalization of the Schrödinger equation in which the spatial derivative is replaced by a suitable convolution operator to prove the existence of a large class of superoscillating sequences. The method we use also allows us to construct such sequences explicitly.