CRM Proceedings & Lecture Notes 1998; 235 pp; softcover Volume: 14 ISBN10: 0821809490 ISBN13: 9780821809495 List Price: US$83 Member Price: US$66.40 Order Code: CRMP/14
 Although originally posed in the context of mathematical problems related to medical imaging, the bispectral problem is now closely related to other topics and has connections to many areas of pure and applied mathematics. 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. Following several years of exciting new results on the subject, in March 1997 the Centre de Recherches Mathématiques held the first scientific meeting devoted exclusively to the bispectral problem. Collected in this volume are contributions from the speakers at this meeting. The participants at this workshop included a majority of those researchers who have made significant contributions to the subject and many others working on related problems. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students, research mathematicians and physicists interested in the bispectral problem. Table of Contents Part 1. Bispectrality  B. Bakalov, E. Horozov, and M. Yakimov  Automorphisms of the Weyl algebra and bispectral operators
 Y. Berest  Huygens' principle and the bispectral problem
 F. A. Grunbaum  Some bispectral musings
 L. Haine  Beyond the classical orthogonal polynomials
 J. Harnad  Bispectral operators, dual isomondromic deformations and the RiemannHilbert dressing method
 A. Kasman  Darboux transformations and the bispectral problem
 F. Levstein and L. F. Matusevich  The discrete version of the bispectral problem
 M. Rothstein  Explicit formulas for the Airy and Bessel bispectral involutions in terms of CalogeroMoser pairs
 V. Spiridonov, L. Vinet, and A. Zhedanov  Bispectrality and Darboux transformations in the theory of orthogonal polynomials
 A. P. Veselov  BakerAkhiezer functions and the bispectral problem in many dimensions
 G. Wilson  Bispectral algebras of ordinary differential operators
 J. P. Zubelli  The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems
Part 2. Related Topics  V. Kac and J. van de Leur  The geometry of spinors and the multicomponent BKP and DKP hierarchies
 F. Magri  The Hamiltonian route to Sato Grassmannian
 V. B. Matveev  Darboux transformations in associative rings and functionaldifference equations
 A. Y. Orlov  Remarks about the CalogeroMoser system and the KP equation
 Subject index
