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Symmetries and Laplacians - 1st Edition - ISBN: 9780444886125, 9780080872858

Symmetries and Laplacians, Volume 174

1st Edition

Introduction to Harmonic Analysis, Group Representations and Applications

Author: D. Gurarie
eBook ISBN: 9780080872858
Imprint: North Holland
Published Date: 18th May 1992
Page Count: 452
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Table of Contents

Basics of Representation Theory. Commutative Harmonic Analysis. Representations of Compact and Finite Groups. Lie Groups SU(2) and SO(3). Classical Compact Lie Groups and Algebras. The Heisenberg Group and Semidirect Products. Representations of SL2. Lie Groups and Hamiltonian Mechanics. Appendices: Spectral Decomposition of Selfadjoint Operators. Integral Operators. A Primer on Riemannian Geometry: Geodesics, Connection, Curvature. References. List of Frequently Used Notations. Index.


Designed as an introduction to harmonic analysis and group representations, this book covers a wide range of topics rather than delving deeply into any particular one. In the words of H. Weyl is primarily meant for the humble, who want to learn as new the things set forth therein, rather than for the proud and learned who are already familiar with the subject and merely look for quick and exact information....

The main objective is to introduce the reader to concepts, ideas, results and techniques that evolve around symmetry-groups, representations and Laplacians. More specifically, the main interest concerns geometrical objects and structures {X}, discrete or continuous, that possess sufficiently large symmetry group G, such as regular graphs (Platonic solids), lattices, and symmetric Riemannian manifolds. All such objects have a natural Laplacian &Dgr;, a linear operator on functions over X, invariant under the group action. There are many problems associated with Laplacians on X, such as continuous or discrete-time evolutions, on X, random walks, diffusion processes, and wave-propagation. This book contains sufficient material for a 1 or 2-semester course.


No. of pages:
© North Holland 1992
18th May 1992
North Holland
eBook ISBN:

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About the Author

D. Gurarie

Affiliations and Expertise

Department of Mathematics and Statistics, Case Western University, Cleveland, OH, USA