Ebook: Compactification of Symmetric Spaces

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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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.

---

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.

Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-13
Subalgebras and Parabolic Subgroups....Pages 14-21
Geometrical Constructions of Compactifications....Pages 22-47
The Satake-Furstenberg Compactifications....Pages 48-73
The Karpelevi? Compactification....Pages 74-94
Martin Compactifications....Pages 95-102
The Martin Compactification X ??X(?0)....Pages 103-115
The Martin Compactification X ? ? X(?)....Pages 116-130
An Intrinsic Approach To The Boundaries of X....Pages 131-156
Compactification via the Ground State....Pages 157-164
Harnack Inequality, Martin’s Method and The Positive Spectrum for Random Walks....Pages 165-185
The Furstenberg Boundary and Bounded Harmonic Functions....Pages 186-194
Integral Representation of Positive Eigenfunctions of Convolution Operators....Pages 195-212
Random Walks and Ground State Properties....Pages 213-230
Extension to Semisimple Algebraic Groups Defined Over a Local Field....Pages 231-236
Back Matter....Pages 237-286

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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.

Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-13
Subalgebras and Parabolic Subgroups....Pages 14-21
Geometrical Constructions of Compactifications....Pages 22-47
The Satake-Furstenberg Compactifications....Pages 48-73
The Karpelevi? Compactification....Pages 74-94
Martin Compactifications....Pages 95-102
The Martin Compactification X ??X(?0)....Pages 103-115
The Martin Compactification X ? ? X(?)....Pages 116-130
An Intrinsic Approach To The Boundaries of X....Pages 131-156
Compactification via the Ground State....Pages 157-164
Harnack Inequality, Martin’s Method and The Positive Spectrum for Random Walks....Pages 165-185
The Furstenberg Boundary and Bounded Harmonic Functions....Pages 186-194
Integral Representation of Positive Eigenfunctions of Convolution Operators....Pages 195-212
Random Walks and Ground State Properties....Pages 213-230
Extension to Semisimple Algebraic Groups Defined Over a Local Field....Pages 231-236
Back Matter....Pages 237-286
....