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Symmetries and Laplacians

Introduction to Harmonic Analysis, Group Representations and Applications

D. Gurarie (Autor)

Buch | Hardcover

462 Seiten

1992
Elsevier Science Ltd (Verlag)
978-0-444-88612-5 (ISBN)

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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 "...it 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 Delta , 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.

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 SL 2 . 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.

Reihe/Serie	Mathematics Studies ; v.174
Verlagsort	Oxford
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-444-88612-5 / 0444886125
ISBN-13	978-0-444-88612-5 / 9780444886125
Zustand	Neuware