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Groups Acting on Hyperbolic Space : Harmonic Analysis and Number Theory - Jurgen Elstrodt

Groups Acting on Hyperbolic Space

Harmonic Analysis and Number Theory

Hardcover Published: 12th November 1997
ISBN: 9783540627456
Number Of Pages: 524

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This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva­ ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n :::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge­ ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauß had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy­ perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries with well-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten­ sion of index 2 of the group PSL(2,

"Das vorliegende Buch hat alle Chancen, eine Standardreferenz zu werden. Es eignet sich sowohl als Nachschlagewerk fur Experten in diesem Bereich als auch als Lekture fur Einsteiger." DMV Jahresbericht, Bd. 103, Heft 1, 2001

Preface
Three-Dimensional Hyperbolic Spacep. 1
Groups Acting Discontinuously on Three-Dimensional Hyperbolic Spacep. 33
Automorphic Functionsp. 83
Spectral Theory of the Laplace Operatorp. 131
Spectral Theory of the Laplace Operator for Cocompact Groupsp. 185
Spectral Theory of the Laplace Operator for Cofinite Groupsp. 231
PSL(2) over Rings of Imaginary Quadratic Integersp. 311
Eisenstein Series for PSL(2) over Imaginary Quadratic Integersp. 359
Integral Binary Hermitian Formsp. 407
Examples of Discontinuous Groupsp. 443
Referencesp. 497
Subject Indexp. 521
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540627456
ISBN-10: 3540627456
Series: Springer Monographs in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 524
Published: 12th November 1997
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 0.88