ARI Guest Talk: 27.06.2024, 10am

Ilya Krishtal (Northern Illinois University, USA) will give a talk on "A Spectral Theory Approach to Prony’s Problem".

At the end of the 18th century Prony created an algorithm that allows one to recover an s-sparse d-dimensional vector from 2s of its consecutive Fourier coefficients (2s < d). This algorithm has seen numerous generalizations and appeared in various other contexts. For example, it has been found useful for understanding concepts such as compressed sensing, super-resolution, and uncertainty principles. In this talk, I will describe a relatively novel approach which regards Prony’s problem as a spectral identification problem for an unknown restriction of a known linear operator. We will see that a Prony-type algorithm applies in a very general context of Banach modules and may be used for problems such as the spectral identification in dynamical sampling and the time-varying channel identification in wireless communication. The talk is based on joint papers with A. Aldroubi and G. Pfander.

Prof. Ilya Krishtal (Department of Mathematical Sciences, Northern Illinois University) is currently visiting the Acoustics Research Institute of the OeAW.