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Softcover ISBN:  9780821809495 
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Softcover ISBN:  9780821809495 
Product Code:  CRMP/14 
List Price:  $93.00 
MAA Member Price:  $83.70 
AMS Member Price:  $74.40 
eBook ISBN:  9781470439286 
Product Code:  CRMP/14.E 
List Price:  $88.00 
MAA Member Price:  $79.20 
AMS Member Price:  $70.40 
Softcover ISBN:  9780821809495 
eBook ISBN:  9781470439286 
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 DetailsCRM Proceedings & Lecture NotesVolume: 14; 1998; 235 ppMSC: 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.ReadershipGraduate 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 RiemannHilbert 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 CalogeroMoser pairs

Bispectrality and Darboux transformations in the theory of orthogonal polynomials

BakerAkhiezer 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 functionaldifference equations

Remarks about the CalogeroMoser system and the KP equation


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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.
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 RiemannHilbert 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 CalogeroMoser pairs

Bispectrality and Darboux transformations in the theory of orthogonal polynomials

BakerAkhiezer 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 functionaldifference equations

Remarks about the CalogeroMoser system and the KP equation