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The Bispectral Problem
 
Edited by: John Harnad Centre de Recherches Mathématiques, Université, Montreal, QC, Canada
Alex Kasman Centre de Recherches Mathématiques, Université, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
The Bispectral Problem
Softcover ISBN:  978-0-8218-0949-5
Product Code:  CRMP/14
List Price: $93.00
MAA Member Price: $83.70
AMS Member Price: $74.40
eBook ISBN:  978-1-4704-3928-6
Product Code:  CRMP/14.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
Softcover ISBN:  978-0-8218-0949-5
eBook: ISBN:  978-1-4704-3928-6
Product Code:  CRMP/14.B
List Price: $181.00 $137.00
MAA Member Price: $162.90 $123.30
AMS Member Price: $144.80 $109.60
The Bispectral Problem
Click above image for expanded view
The Bispectral Problem
Edited by: John Harnad Centre de Recherches Mathématiques, Université, Montreal, QC, Canada
Alex Kasman Centre de Recherches Mathématiques, Université, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Softcover ISBN:  978-0-8218-0949-5
Product Code:  CRMP/14
List Price: $93.00
MAA Member Price: $83.70
AMS Member Price: $74.40
eBook ISBN:  978-1-4704-3928-6
Product Code:  CRMP/14.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
Softcover ISBN:  978-0-8218-0949-5
eBook ISBN:  978-1-4704-3928-6
Product Code:  CRMP/14.B
List Price: $181.00 $137.00
MAA Member Price: $162.90 $123.30
AMS Member Price: $144.80 $109.60
  • Book Details
     
     
    CRM Proceedings & Lecture Notes
    Volume: 141998; 235 pp
    MSC: Primary 33; 34; Secondary 58; 13; 35; 70

    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 co-published with the Centre de Recherches Mathématiques.

    Readership

    Graduate students, research mathematicians and physicists interested in the bispectral problem.

  • Table of Contents
     
     
    • Part 1. Bispectrality
    • Automorphisms of the Weyl algebra and bispectral operators
    • Huygens’ principle and the bispectral problem
    • Some bispectral musings
    • Beyond the classical orthogonal polynomials
    • Bispectral operators, dual isomondromic deformations and the Riemann-Hilbert dressing method
    • Darboux transformations and the bispectral problem
    • The discrete version of the bispectral problem
    • Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs
    • Bispectrality and Darboux transformations in the theory of orthogonal polynomials
    • Baker-Akhiezer functions and the bispectral problem in many dimensions
    • Bispectral algebras of ordinary differential operators
    • The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems
    • Part 2. Related Topics
    • The geometry of spinors and the multicomponent BKP and DKP hierarchies
    • The Hamiltonian route to Sato Grassmannian
    • Darboux transformations in associative rings and functional-difference equations
    • Remarks about the Calogero-Moser system and the KP equation
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 141998; 235 pp
MSC: Primary 33; 34; Secondary 58; 13; 35; 70

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 co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students, research mathematicians and physicists interested in the bispectral problem.

  • Part 1. Bispectrality
  • Automorphisms of the Weyl algebra and bispectral operators
  • Huygens’ principle and the bispectral problem
  • Some bispectral musings
  • Beyond the classical orthogonal polynomials
  • Bispectral operators, dual isomondromic deformations and the Riemann-Hilbert dressing method
  • Darboux transformations and the bispectral problem
  • The discrete version of the bispectral problem
  • Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs
  • Bispectrality and Darboux transformations in the theory of orthogonal polynomials
  • Baker-Akhiezer functions and the bispectral problem in many dimensions
  • Bispectral algebras of ordinary differential operators
  • The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems
  • Part 2. Related Topics
  • The geometry of spinors and the multicomponent BKP and DKP hierarchies
  • The Hamiltonian route to Sato Grassmannian
  • Darboux transformations in associative rings and functional-difference equations
  • Remarks about the Calogero-Moser system and the KP equation
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.