Stoll Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

Erscheinungsjahr 2016
ISBN: 978-1-316-66723-1
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 431, 0 Seiten

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Stoll, Manfred

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Stoll, Manfred
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).