Commuting differential and integral operators and the adelic Grassmannian

Abstract: Beginning with the work of Landau, Pollak and Slepian in the 1960s on time-band limiting, commuting pairs of integral and differential operators have played a key role in signal processing, random matrix theory and integrable systems. In this talk, we will describe a close connection between commuting integral and differential operators and points in the adelic Grassmannian, which provides a commuting pair for each self-adjoint point in the Grassmannian. Central to this relationship is the Fourier algebra, a certain algebra of differential operators isomorphic to the algebra of differential operators on a line bundle over a rational curve.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometryoperator algebras

Audience: researchers in the topic

Analysis and Geometry Seminar