Some Infinite Order Differential Operators Associated with Superoscillations in Several variables

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.