The course treats a collection of threshold phenomena in harmonic analysis, such as completeness problems and uniqueness problems. This includes topics such as Wiener's theorem, Heisenberg's uncertainty principle, and Ivashev-Musatov's theorem. The course provides a comprehensive summary of the theory of Nevannlinna theory from different perspectives on uncertainty principles, with applications to F. and M. Riesz's theorems, Szegö's theorem, and Khrushchev's theorem.
Much of the course content will touch on elements from other mathematical disciplines, such as probability theory, operator theory, potential theory, and fractal geometry.
