Symmetrization in Analysis (New Mathematical Monographs): Series Number 36 - Image 1

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Cambridge University Press Symmetrization in Analysis (New Mathematical Monographs): Series Number 36

Name: Symmetrization in Analysis (New Mathematical Monographs): Series Number 36
Brand: Cambridge University Press
Price: 95.3 GBP
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Mathematical Analysis

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Description

Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from two-point polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding self-contained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough self-contained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric.

Product Specifications

Brand: Cambridge University Press
Format: hardcover
ASIN: 0521830478
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis
Domain: Amazon UK
Release Date: 08 April 2016
Listed Since: 26 September 2006

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Cambridge University Press Symmetrization in Analysis (New Mathematical Monographs): Series Number 36

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