Dynamical sampling for burst-like forcing terms

Analysis Seminar
Wednesday, March 24, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Ilya Krishtal – Northern Illinois University – ikrishtal@niu.eduhttps://www.niu.edu/krishtal/index.shtml
Christopher Heil

Dynamical sampling is a framework for studying the sampling and reconstruction problems for vectors that evolve under the action of a linear operator. In the first part of the talk I will review a few specific problems that have been part of the framework or motivated by it. In the second part of the talk I will concentrate on the problem of recovering a burst-like forcing term in an initial value problem for an abstract first order differential equation on a Hilbert space. We will see how the ideas of dynamical sampling lead to algorithms that allow one to stably and accurately approximate the burst-like portion of a forcing term as long as the background portion is sufficiently smooth.