Chapter 7: A further look at time-and-band limiting for matrix orthogonal polynomials

Abstract

We extend to a situation involving matrix-valued orthogonal polynomials, a scalar result that originates in work of Shannon and a ground-breaking series of papers by Slepian, Landau and Pollak at Bell Labs in the 1960s. While these papers feature integral and differential operators acting on scalar-valued functions, we are dealing here with integral and differential operators acting on matrix-valued functions.