Progress in Mathematics

By: Yves Guivarc'h, Lizhen Ji, John C. Taylor

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Hardcover | 26 August 1998

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304 Pages

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24.77 x 16.51 x 1.91

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The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view.

Key features:

* definition and detailed analysis of the Martin compactifications

* new geometric Compactification, defined in terms of the Tits building, that coincides with the Martin Compactification at the bottom of the positive spectrum.

* geometric, non-inductive, description of the Karpelevic Compactification

* study of the well-know isomorphism between the Satake compactifications and the Furstenberg compactifications

* systematic and clear progression of topics from geometry to analysis, and finally to random walks

The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

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Preface
Introduction	p. 1
Subalgebras and parabolic subgroups	p. 14
Geometrical constructions of compactifications	p. 22
The Satake-Furstenberg compactifications	p. 48
The Karpelevic compactification	p. 74
Martin compactifications	p. 95
The Martin compactification X[actual symbol not reproducible]X([lambda][subscript 0])	p. 103
The Martin compactification X[actual symbol not reproducible]X([lambda][subscript 0])	p. 116
An intrinsic approach to the boundaries of X	p. 131
Compactification via the ground state	p. 157
Harnack inequality, Martin's method and the positive spectrum for random walks	p. 165
The Furstenberg boundary and bounded harmonic functions	p. 186
Integral representation of positive eigenfunctions of convolution operators	p. 195
Random walks and ground state properties	p. 213
Extension to semisimple algebraic groups defined over a local field	p. 231
Table of Contents provided by Blackwell. All Rights Reserved.

Progress in Mathematics

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Hardcover

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