Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

Manfred Stoll

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN: 9781107541481
• eBook ISBN: 9781316667231
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

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.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Dedication
• Table of contents
• Preface
• 1 Möbius Transformations
• 2 Möbius Self-Maps of the Unit Ball
• 3 The Invariant Laplacian, Gradient, and Measure
• 4 [mathcal H]-Harmonic and [mathcal H]-Subharmonic Functions
• 5 The Poisson Kernel and Poisson Integrals
• 6 Spherical Harmonic Expansions
• 7 Hardy-Type Spaces of [mathcal H]-Subharmonic Functions
• 8 Boundary Behavior of Poisson Integrals
• 9 The Riesz Decomposition Theorem for [mathcal H]-Subharmonic Functions
• 10 Bergman and Dirichlet Spaces of [mathcal H]-Harmonic Functions
• References
• Index of Symbols
• Index