Four Aspects of Superoscillations

Abstract

A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: 1. Superoscillations can be generated efficiently and stably through multiplication. 2. There is a win-win situation in the sense that even in circumstances where superoscillations cannot be used for superresolution, they can be useful for what may be called superabsorption, an effective up-conversion of low frequencies 3. The study of superoscillations may be useful for generalizing the Shannon Hartley noisy channel capacity theorem. 4. The phenomenon of superoscillations naturally generalizes beyond bandlimited functions.