About the project
In signal processing, periodic signals can be studied using Fourier series, where the basic building blocks are sine waves. However, when a signal changes substantially over time, such as a piece of music, different methods are needed. Gabor frames provide one such method. A Gabor frame allows for representations of a signal that emphasizes its frequency content at each point in time, similarly to how sheet music is written. When constructing a Gabor frame, a point set in the time-frequency plane needs to be specified. Gabor frames over lattice point sets enjoy a deep duality theory with connections to operator algebras and the representation theory of groups. For non-lattice point sets, these connections are less clear. The aim of this project is to fill this gap in the existing knowledge, associating operator algebras to Gabor frames over a class of point sets known as quasicrystals. In particular, a major goal is to prove existence results for Gabor frames over quasicrystals which generalize known results for lattices.
Financing
This project is financed by the Reseach Council of Norway. Funding ID: 314048