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Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

Harmonic and Subharmonic Function Theory on the Hyperbolic Ball

by Manfred Stoll


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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.

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Product Details

ISBN-13: 9781107541481
Publisher: Cambridge University Press
Publication date: 06/30/2016
Series: London Mathematical Society Lecture Note Series , #431
Pages: 230
Product dimensions: 5.98(w) x 8.98(h) x 0.59(d)

About the Author

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).

Table of Contents

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.

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