LMI Lecture: Super-oscillations and related matters

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.

Lecture 1:

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.