| Description |
1 online resource (xv, 225 pages) |
| Series |
London Mathematical Society lecture note series ; 431 |
|
London Mathematical Society lecture note series ; 431.
|
| Contents |
Möbius transformations -- Möbius self-maps of the unit ball -- The invariant laplacian, gradient, and measure -- Harmonic and subharmonic functions -- The Poisson kernel and Poisson integrals -- Spherical harmonic expansions -- Hardy-type spaces of subharmonic functions -- Boundary behavior of Poisson integrals -- The Riesz decomposition theorem for subharmonic functions -- Bergman and Dirichlet spaces of harmonic functions |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Print version record |
| Subject |
Harmonic functions.
|
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Subharmonic functions.
|
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Hyperbolic spaces.
|
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
|
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Funciones armónicas
|
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Geometría hiperbólica
|
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Harmonic functions
|
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Hyperbolic spaces
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Subharmonic functions
|
| Form |
Electronic book
|
| ISBN |
9781316341063 |
|
1316341062 |
|
