Abstract
Slepian, Landau, and Pollak found that a certain finite integral operator commutes with a much simpler second-order differential operator. The eigenfunctions that these operators share are prolate spheroidal wave functions and the study of these eigenfunctions has led to applications in several areas. Grunbaum displayed analogues of this commutativity for certain integral operators involving orthogonal polynomials. We discuss some implications of this commutativity for these eigenfunctions.
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