Discrete and continuous frames

Daniel Freeman, Saint Louis University

3:30 pm - 4:30 pm, PHSC 1105

There is a close relationship and long history between discrete and continuous frames for Hilbert spaces. In particular, the standard method to study continuous frames that arise in physics (more commonly known as coherent states) is to sample them to obtain an orthonormal basis or frame. The Discretization Problem asks if every continuous frame can be sampled to obtain a discrete frame. We will discuss what makes this challenging, how to reduce it to a problem solely about partitioning discrete frames, and how the partitioning problem can be solved using the tools developed in the recent solution of the Kadison-Singer problem. This is joint work with Darrin Speegle.