000 02514nam a22003738i 4500
001 CR9781139020244
003 UkCbUP
005 20200124160157.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 110216s2019||||enk o ||1 0|eng|d
020 _a9781139020244 (ebook)
020 _z9780521830478 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA300
_b.B1685 2019
082 0 0 _a515/.22
_223
100 1 _aBaernstein, Albert,
_cII,
_d1941-2014,
_eauthor.
245 1 0 _aSymmetrization in analysis /
_cAlbert Baernstein II ; with David Drasin, Richard Laugesen.
264 1 _aCambridge :
_bCambridge University Press,
_c2019.
300 _a1 online resource (xviii, 473 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aNew mathematical monographs ;
_v36
500 _aTitle from publisher's bibliographic system (viewed on 25 Feb 2019).
520 _aSymmetrization 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.
650 0 _aMathematical analysis.
650 0 _aSymmetric functions.
700 1 _aDrasin, D.
_q(David),
_d1940-
_eauthor.
700 1 _aLaugesen, Richard,
_d1967-
_eauthor.
776 0 8 _iPrint version:
_z9780521830478
830 0 _aNew mathematical monographs ;
_v36.
856 4 0 _uhttps://doi.org/10.1017/9781139020244
999 _c514526
_d514524