Analysis seminar
Speaker: Alejandro Chavez-Dominguez (University of Oklahoma)
Title: Dynamical sampling on Banach spaces
Abstract: Dynamical sampling is a paradigm in signal processing based on the following desirable spatio-temporal trade-off: instead of recovering a signal by measuring it at many different locations at the same time (requiring multiple sensors), we would like to be able to recover it by measuring it only at one location but at many different times (requiring only one sensor).
In the Hilbert space setting, frames (a generalization of orthonormal bases) are a well-established method of doing signal recovery. The dynamical sampling question can then be shown to translate to: for which bounded linear operators on a Hilbert space does there exist an orbit which is a frame? This question has by now been fully answered, together with other closely related ones.
Using the notion of Schauder frames for Banach spaces, we explore several versions of dynamical sampling questions in this context and prove various results reminiscent of the classical ones. While some of these results are less explicit, they are easier to understand conceptually. This is joint work in progress with Daniel Carando (U. of Buenos Aires).