The Bispectral Problem

Abstract

Part 1. Bispectrality: Automorphisms of the Weyl algebra and bispectral operators by B. Bakalov, E. Horozov, and M. Yakimov Huygens' principle and the bispectral problem by Y. Berest Some bispectral musings by F. A. Grunbaum Beyond the classical orthogonal polynomials by L. Haine Bispectral operators, dual isomondromic deformations and the Riemann-Hilbert dressing method by J. Harnad Darboux transformations and the bispectral problem by A. Kasman The discrete version of the bispectral problem by F. Levstein and L. F. Matusevich Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs by M. Rothstein Bispectrality and Darboux transformations in the theory of orthogonal polynomials by V. Spiridonov, L. Vinet, and A. Zhedanov Baker-Akhiezer functions and the bispectral problem in many dimensions by A. P. Veselov Bispectral algebras of ordinary differential operators by G. Wilson The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems by J. P. Zubelli Part 2. Related Topics: The geometry of spinors and the multicomponent BKP and DKP hierarchies by V. Kac and J. van de Leur The Hamiltonian route to Sato Grassmannian by F. Magri Darboux transformations in associative rings and functional-difference equations by V. B. Matveev Remarks about the Calogero-Moser system and the KP equation by A. Y. Orlov Subject index.