Analysis Seminar: "Superoscillations and infinite order differential operators"

Abstract: Superoscillations are sequences of band-limited functions that converge to functions with arbitrary large frequencies. They were first identified by Y.Aharonov as a byproduct of his notion of weak measurement in quantum mechanics. An important question is to learn whether the superoscillatory behavior persists when a superoscillating sequence is taken as initial value for the Cauchy problem for a given Schrodinger equation. In this talk I will give the basic notions on superoscillations, and I will show the approach that is used to study the persistence of such behavior. As it turns out, the tools necessary to demonstrate superoscillations longevity come from the theory of entire functions with growth conditions and the infinite order differential operators of which they are symbols.

Host: Steven Krantz