250147 SE Frame Theory (2020W)

Frame theory is concerned with the study of stable, potentially overcomplete spanning sets in a Hilbert space. Its starting point is a generalization of the principle of an orthonormal basis resulting in the definition of a frame. Similar to orthonormal bases (ONBs) every function can be (i) recovered from its frame coefficients, i.e. the inner products with respect to the frame elements and (ii) expanded into a linear combination of the frame elements. Frames have a rich structure despite being much less restrictive than ONBs, rendering them attractive for a wide number of applications. In addition to being an active field of research, posing interesting research questions of its own, frame theory has applications in other fields, like signal processing and physics.

In this seminar the topics will go beyond basic frame theory (treated in last years course 'frame theory'). We study and discuss selected advanced topics in frame theory and its application. The choice of topics will be discussed during the seminar.