Symmetrization in analysis /
Baernstein, Albert, II, 1941-2014,
Symmetrization in analysis / Albert Baernstein II ; with David Drasin, Richard Laugesen. - 1 online resource (xviii, 473 pages) : digital, PDF file(s). - New mathematical monographs ; 36 . - New mathematical monographs ; 36. .
Title from publisher's bibliographic system (viewed on 25 Feb 2019).
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.
9781139020244 (ebook) 1139020242 (ebook) 9781108615112 1108615112
Mathematical analysis.
Symmetric functions.
Control theory.
Integral equations.
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books.
QA300 / .B1685 2019
515/.22
Symmetrization in analysis / Albert Baernstein II ; with David Drasin, Richard Laugesen. - 1 online resource (xviii, 473 pages) : digital, PDF file(s). - New mathematical monographs ; 36 . - New mathematical monographs ; 36. .
Title from publisher's bibliographic system (viewed on 25 Feb 2019).
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.
9781139020244 (ebook) 1139020242 (ebook) 9781108615112 1108615112
Mathematical analysis.
Symmetric functions.
Control theory.
Integral equations.
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books.
QA300 / .B1685 2019
515/.22