Overview

The central theme of this book is the search for solutions to eigenvalue problems that satisfy additional equations in the spectral parameter, for example, pairs of eigenvalue equations. This problem, which looks very simple at first, has turned out to be both deep and difficult. Moreover, this concept of bispectrality has been shown to be useful in many active areas of current research in mathematics and physics.

Full Product Details

Author:   John Harnad ,  Alex Kasman
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 14
Weight:   0.431kg
ISBN:  

9780821809495

ISBN 10:   0821809490
Pages:   235
Publication Date:   28 February 1998
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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