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 Mathematiques 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.
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978-0-8218-0949-5 (9780821809495)
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Schweitzer Klassifikation
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.
