Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.

Manfred Stoll (Author)

9781107541481, Cambridge University Press

Paperback / softback, published 30 June 2016

230 pages, 100 exercises
22.8 x 15.2 x 1.5 cm, 0.37 kg

'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

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.

Subject Areas: Functional analysis & transforms [PBKF], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]