| Softcover ISBN: | 978-0-8218-1692-9 |
| Product Code: | CBMS/42 |
| List Price: | $23.00 |
| Individual Price: | $18.40 |
| eBook ISBN: | 978-1-4704-2402-2 |
| Product Code: | CBMS/42.E |
| List Price: | $20.00 |
| Individual Price: | $16.00 |
| Softcover ISBN: | 978-0-8218-1692-9 |
| eBook: ISBN: | 978-1-4704-2402-2 |
| Product Code: | CBMS/42.B |
| List Price: | $43.00 $33.00 |
| Softcover ISBN: | 978-0-8218-1692-9 |
| Product Code: | CBMS/42 |
| List Price: | $23.00 |
| Individual Price: | $18.40 |
| eBook ISBN: | 978-1-4704-2402-2 |
| Product Code: | CBMS/42.E |
| List Price: | $20.00 |
| Individual Price: | $16.00 |
| Softcover ISBN: | 978-0-8218-1692-9 |
| eBook ISBN: | 978-1-4704-2402-2 |
| Product Code: | CBMS/42.B |
| List Price: | $43.00 $33.00 |
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Book DetailsCBMS Regional Conference Series in MathematicsVolume: 42; 1980; 59 ppMSC: Primary 22; Secondary 33
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Table of Contents
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Chapters
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Introduction
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Representations of SU(2)
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The general theory of linear representations of compact groups
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Lie theory of representations of compact connected Lie groups
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Induced representations of compact groups
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Spherical functions on compact groups
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Examples; spherical harmonics
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The general theory of spherical functions
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Fourier and Plancherel transforms
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Extension of the Plancherel transform
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The subtleties of harmonic analysis
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Differential properties of spherical functions on Lie groups
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Spherical functions on semisimple Lie groups
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More on SL(2, $\mathbb {R}$)
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Automorphic functions
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Groups of isometries and Bessel functions
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Other special functions
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
-
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
