Harmonic and Subharmonic Function Theory on the Hyperbolic Ball (London Mathematical Society Lecture Note Series)
Cambridge University Press, 6/30/2016
EAN 9781107541481, ISBN10: 1107541484
Paperback, 242 pages, 22.8 x 15.2 x 1.5 cm
Language: English
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.
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.