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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
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List Price: $31.50 Click above image for expanded view 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;

• 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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