Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

AUTHOR: Manfred Stoll



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

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.



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