UID:
almafu_9960117314102883
Format:
1 online resource (xv, 225 pages) :
,
digital, PDF file(s).
ISBN:
1-316-66618-2
,
1-316-66708-1
,
1-316-66723-5
,
1-316-66738-3
,
1-316-66753-7
,
1-316-66798-7
,
1-316-34106-2
Series Statement:
London Mathematical Society lecture note series ; 431
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 06 Jun 2016).
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Cover ; Series information; Title page; Copyright information; Dedication; Table of contents; Preface; 1 Möbius Transformations; 1.1 Notation; 1.2 Inversion in Spheres and Planes; 1.3 Möbius Transformations; 2 Möbius Self-Maps of the Unit Ball; 2.1 Möbius Transformations of [mathbb B]; 2.2 The Hyperbolic Metric on [mathbb B]; 2.3 Hyperbolic Half-Space [mathbb H]; 2.4 Exercises; 3 The Invariant Laplacian, Gradient, and Measure; 3.1 The Invariant Laplacian and Gradient; 3.2 The Fundamental Solution of [Delta sub(h)]; 3.3 The Invariant Measure on [mathbb B]
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9.2 Applications of the Riesz Decomposition Theorem9.3 Integrability of [mathcal H]-Superharmonic Functions; 9.4 Boundary Limits of Green Potentials; 9.5 Non-tangential Limits of [mathcal H]-Subharmonic Functions; 9.6 Exercises; 10 Bergman and Dirichlet Spaces of [mathcal H]-Harmonic Functions; 10.1 Properties of [mathcal D sub(γ) sup(p)] and [mathcal B sub(γ) sup(p)]; 10.2 Möbius Invariant Spaces; 10.3 Equivalence of [mathcal B sup(p) sub(γ)] and [mathcal D sup(p) sub(γ)] for γ 〉 (n-1); 10.4 Integrability of Functions in [mathcal B sup(p) sub(γ) and [mathcal D sup(p) sub(γ)]
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10.5 Integrability of Eigenfunctions of [Delta sub(h)]
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English
Additional Edition:
ISBN 1-107-54148-4
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9781316341063
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