Symmetrization in analysis:
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, frequ...
Gespeichert in:
| Beteilige Person: | |
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| Weitere beteiligte Personen: | , |
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2019
|
| Schriftenreihe: | New mathematical monographs
36 |
| Links: | https://doi.org/10.1017/9781139020244 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xviii, 473 Seiten) |
| ISBN: | 9781139020244 |
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| 520 | |a 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. | ||
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| spelling | Baernstein, Albert 1941-2014 Symmetrization in analysis Albert Baernstein II ; with David Drasin, Richard Laugesen Cambridge Cambridge University Press 2019 1 Online-Ressource (xviii, 473 Seiten) txt c cr New mathematical monographs 36 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. Drasin, D. 1940- Laugesen, Richard 1967- Erscheint auch als Druck-Ausgabe 9780521830478 |
| spellingShingle | Baernstein, Albert 1941-2014 Symmetrization in analysis |
| title | Symmetrization in analysis |
| title_auth | Symmetrization in analysis |
| title_exact_search | Symmetrization in analysis |
| title_full | Symmetrization in analysis Albert Baernstein II ; with David Drasin, Richard Laugesen |
| title_fullStr | Symmetrization in analysis Albert Baernstein II ; with David Drasin, Richard Laugesen |
| title_full_unstemmed | Symmetrization in analysis Albert Baernstein II ; with David Drasin, Richard Laugesen |
| title_short | Symmetrization in analysis |
| title_sort | symmetrization in analysis |
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