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Other titles in the London Mathematical Society Lecture Notes series:

Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note)

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Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note) Cover

 

Synopses & Reviews

Publisher Comments:

This monograph covers Poisson-Szegö integrals on the ball, the Green's function for ^D*D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. It also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Greens potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included.

Synopsis:

Topics covered include Poisson-Szegö integrals on the ball, the Green's function for ^D*D and the Riesz decomposition theorem for invariant subharmonic functions in this introduction and survey of recent results in potential theory with respect to the Laplace-Beltrami operator ^D*D in several complex variables, with special emphasis on the unit ball in Cn.

Synopsis:

The results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn.

Description:

Includes bibliographical references (p. [164]-169) and index.

Table of Contents

1. Notation and preliminary results; 2. The Bergman kernel; 3. The Laplace-Beltrami operator; 4. Invariant harmonic and subharmonic functions; 5. Poisson-Szegö integrals; 6. The Riesz decomposition theorem; 7. Admissible boundary limits of Poisson integrals; 8. Radial and admissible boundary limits of potentials; 9. Gradient estimates and Riesz potentials; 10. Spaces of invariant harmonic functions; References.

Product Details

ISBN:
9780521468305
Editor:
Cassels, J. W. S.
Editor:
Hitchin, N. J.
Editor:
Cassels, J. W. S.
Editor:
Hitchin, N. J.
Author:
Stoll, Manfred
Author:
Cassels, J. W. S.
Publisher:
Cambridge University Press
Location:
Cambridge ;
Subject:
General
Subject:
Calculus
Subject:
Differential Equations
Subject:
Probability
Subject:
Invariants
Subject:
Potential theory (mathematics)
Subject:
Unit ball.
Subject:
Potential theory
Subject:
Probability & Statistics - General
Subject:
Mathematics-Calculus
Subject:
Algebra - Abstract
Edition Description:
Trade paper
Series:
London Mathematical Society lecture note series ;
Series Volume:
199
Publication Date:
20030631
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
184
Dimensions:
8.97x6.03x.48 in. .60 lbs.

Related Subjects

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Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Invariant Potential Theory in the Unit Ball of Cn (London Mathematical Society Lecture Note) New Trade Paper
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Product details 184 pages Cambridge University Press - English 9780521468305 Reviews:
"Synopsis" by , Topics covered include Poisson-Szegö integrals on the ball, the Green's function for ^D*D and the Riesz decomposition theorem for invariant subharmonic functions in this introduction and survey of recent results in potential theory with respect to the Laplace-Beltrami operator ^D*D in several complex variables, with special emphasis on the unit ball in Cn.
"Synopsis" by , The results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn.
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