Evolution of Superoscillations in the Klein-Gordon Field
Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. There is nowadays a large literature on the evolution of superoscillations under Schrödinger equation with different type of potentials. In this paper, we study the evolution of superoscillations under the Klein-Gordon equation and we describe in precise mathematical terms in what sense superoscillations persist in time during the evolution. The main tools for our investigation are convolution operators acting on spaces of entire functions and Green functions.
Aharonov, Y., Colombo, F., Sabadini, I. et al. Evolution of Superoscillations in the Klein-Gordon Field. Milan J. Math. (2020). https://doi.org/10.1007/s00032-020-00310-x