Abstract This paper aims to contribute to the theory of superoscillations and supershifts. It provides an overview and new insights into the theory. A crucial role in the evolution of superoscillations and supershifts is played by infinite-order differential operators acting on a suitable class of holomorphic functions. In this work, we consider partial differential equations with a convolution term and determine the corresponding expressions for their associated infinite-order operators. We also consider linear partial differential-difference equations, defining the associated infinite-order differential operator in this case.
Colombo et al. (Tue,) studied this question.