The prolate spheroidal phenomena and bispectrality

Details The prolate spheroidal phenomena and bispectrality The prolate spheroidal phenomena and bispectrality

2003-03-17

arxiv.org/abs/math-ph/0303041v1

Physics

Mathematical Physics

12 pages, AMS Latex

Scientific paper

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.

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