02345nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001600128100003200144245010400176264007100280300004100351336002600392337002600418338003600444490003800480500001300518520117400531650002701705650002501732700002401757700003101781856005201812932003201864596000601896949010501902CR9781139020244UkCbUP110216s2019||||enk o ||1 0|eng|d a9781139020244 a9780521830478 a(Sirsi) a792151 aeng00a515/.222231 aBaernstein, Albert,eauthor10aSymmetrization in analysish[E-Book] /cAlbert Baernstein II ; with David Drasin, Richard Laugesen. 1aCambridge :bCambridge University Press,c2019e(CUP)fCUP20200108 a1 online resource (xviii, 473 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aNew mathematical monographs ;v36 aenglisch 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. 0aMathematical analysis. 0aSymmetric functions.1 aDrasin, D.,eauthor1 aLaugesen, Richard,eauthor40uhttps://doi.org/10.1017/9781139020244zVolltext aCambridgeCore (Order 30059) a1 aXX(792151.1)wAUTOc1i792151-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE