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Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

$81.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: July 2016
  • availability: In stock
  • format: Paperback
  • isbn: 9781107541481

$ 81.99 (C)
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About the Authors
  • This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.

    • Opens up the subject to a broader audience by developing the material without requiring a knowledge of differential geometry and Lie groups
    • Self-contained so that the reader does not need to refer constantly to outside references
    • Contains exercises and open problems, ideal for a graduate course
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    Reviews & endorsements

    'The author gives a comprehensive treatment of invariant potential theory. The exposition is clear and elementary. This book is recommended to graduate students and researchers interested in this field. It is a very good addition to the mathematical literature.' Hiroaki Aikawa, MathSciNet

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    Product details

    • Date Published: July 2016
    • format: Paperback
    • isbn: 9781107541481
    • length: 230 pages
    • dimensions: 228 x 152 x 15 mm
    • weight: 0.37kg
    • contains: 100 exercises
    • availability: In stock
  • Table of Contents

    Preface
    1. Möbius transformations
    2. Möbius self-maps of the unit ball
    3. Invariant Laplacian, gradient and measure
    4. H-harmonic and H-subharmonic functions
    5. The Poisson kernel
    6. Spherical harmonic expansions
    7. Hardy-type spaces
    8. Boundary behavior of Poisson integrals
    9. The Riesz decomposition theorem
    10. Bergman and Dirichlet spaces
    References
    Index of symbols
    Index.

  • Author

    Manfred Stoll, University of South Carolina
    Manfred Stoll is Distinguished Professor Emeritus in the Department of Mathematics at the University of South Carolina. His books include Invariant Potential Theory in the Unit Ball of Cn (Cambridge, 1994) and Introduction to Real Analysis (1997).

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