The prolate spheroidal phenomena and bispectrality

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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.
12 pages, AMS Latex

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Mathematical Physics, Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/57330

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0303041
 http://arxiv.org/abs/math-ph/0303041

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arXiv