Harmonic and Subharmonic Function Theory on the Hyperbolic Ball
Harmonic and Subharmonic Function Theory on the Hyperbolic Ball
AUD$97.23
exc GSTThis 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
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
Product details
June 2016Paperback
9781107541481
230 pages
228 × 152 × 15 mm
0.37kg
100 exercises
Available
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.
