Achim Kempf | University of Waterloo, Applied Mathematics
Superoscillations: Faster than Fourier
Counterintuitively, there are smooth and square integrable functions that locally oscillate much faster than the fastest Fourier component that they contain. I will show new state-of-the-art methods that my students developed for constructing such superoscillatory functions. Superoscillations are of both theoretical and applied interest, ranging from applications in optics to the foundations of quantum theory. Information theoretically, signals with superoscillations are consistent with Shannon's noisy channel capacity theorem in a highly nontrivial way that leads to new information-theoretic insights.