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Special Functions and Linear Representations of Lie Groups
 
A co-publication of the AMS and CBMS
Front Cover for Special Functions and Linear Representations of Lie Groups
Available Formats:
Softcover ISBN: 978-0-8218-1692-9
Product Code: CBMS/42
59 pp 
List Price: $21.00
Individual Price: $16.80
Electronic ISBN: 978-1-4704-2402-2
Product Code: CBMS/42.E
59 pp 
List Price: $19.00
Individual Price: $15.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $31.50
Front Cover for Special Functions and Linear Representations of Lie Groups
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Special Functions and Linear Representations of Lie Groups
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN:  978-0-8218-1692-9
Product Code:  CBMS/42
59 pp 
List Price: $21.00
Individual Price: $16.80
Electronic ISBN:  978-1-4704-2402-2
Product Code:  CBMS/42.E
59 pp 
List Price: $19.00
Individual Price: $15.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $31.50
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 421980
    MSC: Primary 22; Secondary 33;
  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Representations of SU(2)
    • The general theory of linear representations of compact groups
    • Lie theory of representations of compact connected Lie groups
    • Induced representations of compact groups
    • Spherical functions on compact groups
    • Examples; spherical harmonics
    • The general theory of spherical functions
    • Fourier and Plancherel transforms
    • Extension of the Plancherel transform
    • The subtleties of harmonic analysis
    • Differential properties of spherical functions on Lie groups
    • Spherical functions on semisimple Lie groups
    • More on SL(2, $\mathbb {R}$)
    • Automorphic functions
    • Groups of isometries and Bessel functions
    • Other special functions
  • Reviews
     
     
    • Presented in a clear, self-contained, and well-organized way, these introductory level lectures are highly recommended for individual or in-class use for acquiring basic knowledge of the groups \({\mathbf SU}(2)\), \({\mathbf SO}(3)\), \({\mathbf SL}(2, \mathbf R)\), and their function theories. Covering representations of \({\mathbf SU}(2)\), spherical harmonics on \(S_n\), representations of the group \({\mathbf SL}(2, \mathbf R)\) and spherical functions with respect to its maximal compact subgroup \({\mathbf SO}(2)\), these lectures also take account of some well known functions exhibited as spherical or matrix-entry functions of unitary representations—for example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\).

      C. F. Dunkl, Mathematical Reviews
  • Request Review Copy
Volume: 421980
MSC: Primary 22; Secondary 33;
  • Chapters
  • Introduction
  • Representations of SU(2)
  • The general theory of linear representations of compact groups
  • Lie theory of representations of compact connected Lie groups
  • Induced representations of compact groups
  • Spherical functions on compact groups
  • Examples; spherical harmonics
  • The general theory of spherical functions
  • Fourier and Plancherel transforms
  • Extension of the Plancherel transform
  • The subtleties of harmonic analysis
  • Differential properties of spherical functions on Lie groups
  • Spherical functions on semisimple Lie groups
  • More on SL(2, $\mathbb {R}$)
  • Automorphic functions
  • Groups of isometries and Bessel functions
  • Other special functions
  • Presented in a clear, self-contained, and well-organized way, these introductory level lectures are highly recommended for individual or in-class use for acquiring basic knowledge of the groups \({\mathbf SU}(2)\), \({\mathbf SO}(3)\), \({\mathbf SL}(2, \mathbf R)\), and their function theories. Covering representations of \({\mathbf SU}(2)\), spherical harmonics on \(S_n\), representations of the group \({\mathbf SL}(2, \mathbf R)\) and spherical functions with respect to its maximal compact subgroup \({\mathbf SO}(2)\), these lectures also take account of some well known functions exhibited as spherical or matrix-entry functions of unitary representations—for example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\).

    C. F. Dunkl, Mathematical Reviews
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