The prolate spheroidal phenomena and bispectrality
arXiv:math-ph/0303041
Abstract
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
References in corpus (6)
- Level-Spacing Distributions and the Airy Kernel
- Fredholm Determinants, Differential Equations and Matrix Models
- Integrable Fredholm Operators and Dual Isomonodromic Deformations
- General methods for constructing bispectral operators
- Bispectral algebras of commuting ordinary differential operators
- Bispectral Darboux Transformations: The Generalized Airy Case