Symmetries and Laplacians: Introduction to Harmonic Analysis, Group Representations and Applications - Brossura

Gurarie, David

Brossura

ISBN 10: 0486462889 ISBN 13: 9780486462882

Casa editrice: Dover Pubns, 2008

Riassunto

Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area.
Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.

Su questo libro

Contenuti

Introduction 1. Basics of representation theory 2. Commutative Harmonic analysis 3. Representations of compact and finite groups 4. Lie groups SU(2) and SO(3) 5. Classical compact Lie groups and algebras 6. The Heisenberg group and semidirect products 7. Representations of SL2 8. Lie groups and hamiltonian mechanics Appendices: Spectral decomposition of selfadjoint operators; integral operators; a primer on Riemannian geometry References List of frequently used notations Index

Product Description

This introductory text examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory. Topics include commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. 1992 edition.

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0486462889
• ISBN 13: 9780486462882
• Rilegatura: Copertina flessibile
• Numero di pagine: 453
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia