LMI Lecture: Super-oscillations and related matters
Prof. Sir Michael Berry, FRS, University of Bristol, UK
This series of lectures concerns a substantial and fast-developing new area, linking a number of what were thought to be separate subjects: quantum physics, optical singularities, mathematical function theory, super-resolution microscopy, radar theory... These are subjects that do not form part of the usual student or Ph.D courses, but can be explained without too much high-power theory, and provide a wonderful illustration of the unity of different areas of mathematics and physics.
Basics, simple examples of functions varying faster than their fastest Fourier components, reproducing fractals, definitions of local momentum, shifted Fourier transforms, relations to Wigner and Husimi functions.