Compactification of Symmetric Spaces

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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. The ...
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Overview

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. 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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Editorial Reviews

Booknews
Investigates the interrelationships of the perspectives on the compactifications that have been developed in the contexts of representation theory, geometry, and random walks, with a view to resolving the differences. Defines and analyzes in detail the Martin version, describes new geometric versions defined in terms of the Tits building, and looks at the well known isomorphism between the Satake and the Furstenberg versions. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Ch. I Introduction 1
Ch. II Subalgebras and parabolic subgroups 14
Ch. III Geometrical constructions of compactifications 22
Ch. IV The Satake-Furstenberg compactifications 48
Ch. V The Karpelevic compactification 74
Ch. VI Martin compactifications 95
Ch. VII The Martin compactification X[actual symbol not reproducible]X([lambda][subscript 0]) 103
Ch. VIII The Martin compactification X[actual symbol not reproducible]X([lambda][subscript 0]) 116
Ch. IX An intrinsic approach to the boundaries of X 131
Ch. X Compactification via the ground state 157
Ch. XI Harnack inequality, Martin's method and the positive spectrum for random walks 165
Ch. XII The Furstenberg boundary and bounded harmonic functions 186
Ch. XIII Integral representation of positive eigenfunctions of convolution operators 195
Ch. XIV Random walks and ground state properties 213
Ch. XV Extension to semisimple algebraic groups defined over a local field 231
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