Harmonic and Subharmonic Function Theory on the Hyperbolic Ball
Published on 15. June 2016
978-1-316-66723-1 (ISBN)
Description
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.
Reviews / Votes
'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, MathSciNetMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 100 Plates, color
File size
1359,99 MB
ISBN-13
978-1-316-66723-1 (9781316667231)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
06/2016
Cambridge University Press
€74.50
Shipment within 15-20 days
Person
Manfred Stoll is Distinguished Professor Emeritus in the Department of Mathematics at the University of South Carolina. His books include Invariant Potential Theory in the Unit Ball of Cn (Cambridge, 1994) and Introduction to Real Analysis (1997).
Content
Preface; 1. Moebius transformations; 2. Moebius 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.
