  Landau, Pollak, Slepian, and Tracy, Widom discovered that certain integral
operators with so called Bessel and Airy kernels possess commuting differential
operators and found important applications of this phenomena in time-band
limiting and random matrix theory. In this paper we announce that very large
classes of integral operators derived from bispectral algebras of rank 1 and 2
(parametrized by lagrangian grassmannians of infinitely large size) have this
property. The above examples come from special points in these grassmannians.
