Time and band limiting for matrix valued functions: an integral and a commuting differential operator

Abstract

The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the $1960$'s, by exploiting a "miracle": a certain naturally appearing integral operator commutes with an explicit differential one. Here we show that this same miracle holds in a matrix valued version of the same problem.

References in corpus (2)

• Spherical Slepian functions and the polar gap in geodesy
• Time and Band Limiting for Matrix Valued Functions, an Example

Cited by in corpus (7)

• Bispectrality and Time-Band-Limiting: Matrix valued polynomials
• $2\times 2$ Hypergeometric operators with diagonal eigenvalues
• A new commutativity property of exceptional orthogonal polynomials
• Commuting integral and differential operators and the master symmetries of the Korteweg-de Vries equation
• Time and band limiting for exceptional polynomials
• Structural formulas for matrix-valued orthogonal polynomials related to $2\times 2$ hypergeometric operators
• The bispectral problem, the Darboux process, monodromy and the Hermite operator