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Compactifications of Symmetric Spaces

  • Book
  • © 1998

Overview

Authors:
  1. Yves Guivarc’h

    1. IRMAR UFR Mathématiques, Université de Rennes-I, Rennes, France

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  2. Lizhen Ji

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

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    You can also search for this author in PubMed   Google Scholar

  3. J. C. Taylor

    1. Department of Mathematics and Statistics, McGill University, Quebec, Canada

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Part of the book series: Progress in Mathematics (PM, volume 156)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 1-13

  3. Subalgebras and Parabolic Subgroups

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 14-21

  4. Geometrical Constructions of Compactifications

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 22-47

  5. The Satake-Furstenberg Compactifications

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 48-73

  6. The Karpelevič Compactification

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 74-94

  7. Martin Compactifications

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 95-102

  8. The Martin Compactification X ∪∂X(λ0)

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 103-115

  9. The Martin Compactification X ∪ ∂ X(λ)

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 116-130

  10. An Intrinsic Approach To The Boundaries of X

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 131-156

  11. Compactification via the Ground State

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 157-164

  12. Harnack Inequality, Martin’s Method and The Positive Spectrum for Random Walks

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 165-185

  13. The Furstenberg Boundary and Bounded Harmonic Functions

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 186-194

  14. Integral Representation of Positive Eigenfunctions of Convolution Operators

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 195-212

  15. Random Walks and Ground State Properties

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 213-230

  16. Extension to Semisimple Algebraic Groups Defined Over a Local Field

    • Yves Guivarc’h, Lizhen Ji, J. C. Taylor
    Pages 231-236

  17. Back Matter

    Pages 237-286
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Keywords

About this book

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.

Authors and Affiliations

  • IRMAR UFR Mathématiques, Université de Rennes-I, Rennes, France

    Yves Guivarc’h

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Lizhen Ji

  • Department of Mathematics and Statistics, McGill University, Quebec, Canada

    J. C. Taylor

Bibliographic Information

  • Book Title: Compactifications of Symmetric Spaces

  • Authors: Yves Guivarc’h, Lizhen Ji, J. C. Taylor

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-2452-5

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1998

  • Hardcover ISBN: 978-0-8176-3899-3Published: 26 August 1998

  • Softcover ISBN: 978-1-4612-7542-8Published: 20 September 2011

  • eBook ISBN: 978-1-4612-2452-5Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XIII, 286

  • Topics: Geometry, Topology

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