Band and time limiting and Heun operators

Band and time restriction of the Fourier transofrm was proposed by Landau, Pollak and Slepian more than 60 years ago. This formalism was generalized by A. Grunbaum for other types of bispectral problems including classical orthogonal polynomials. This problem has important applications in signal processing and tomography. The central mathematical object of the theory is a second order differential or difference operator commuting with a restriction operator. We show that this operator is a special case of the algebraic Heun operator associated with any bispectral system.