# A further look at time-and-band limiting for matrix orthogonal polynomials

## TL;DR

This paper extends classical scalar results on time-and-band limiting to matrix-valued orthogonal polynomials, involving new integral and differential operators acting on matrix functions.

## Contribution

It introduces a novel extension of scalar time-and-band limiting results to matrix orthogonal polynomials with associated integral and differential operators.

## Key findings

- Extension of scalar time-band limiting results to matrix case
- Development of new integral and differential operators for matrix functions
- Foundation for further research in matrix-valued signal processing

## Abstract

We extend to a situation involving matrix valued orthogonal polynomials a scalar result that originates in work of Claude Shannon and a ground-breaking series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's. 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.