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000711942 020__ $$a9783034808743$$qelectronic book
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000711942 0247_ $$a10.1007/978-3-0348-0874-3$$2doi
000711942 035__ $$aSP(OCoLC)ocn893857980
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000711942 08204 $$a516.3/62$$223
000711942 1001_ $$aAlesker, Semyon,$$eauthor.
000711942 24510 $$aIntegral geometry and valuations$$h[electronic resource] /$$cSemyon Alesker, Joseph H.G. Fu ; editors for this volume: Eduardo Gallego, Gil Solanes.
000711942 264_1 $$aBasel :$$bBirkhäuser,$$c2014.
000711942 300__ $$a1 online resource (viii, 112 pages).
000711942 336__ $$atext$$btxt$$2rdacontent
000711942 337__ $$acomputer$$bc$$2rdamedia
000711942 338__ $$aonline resource$$bcr$$2rdacarrier
000711942 4901_ $$aAdvanced courses in mathematics, CRM Barcelona,$$x2297-0304
000711942 504__ $$aIncludes bibliographical references.
000711942 5050_ $$aPart I: New Structures on Valuations and Applications -- Translation invariant valuations on convex sets -- Valuations on manifolds -- Part II: Algebraic Integral Geometry -- Classical integral geometry -- Curvature measures and the normal cycle -- Integral geometry of euclidean spaces via Alesker theory -- Valuations and integral geometry on isotropic manifolds -- Hermitian integral geometry.
000711942 506__ $$aAccess limited to authorized users.
000711942 520__ $$aValuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces.
000711942 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 27, 2014).
000711942 650_0 $$aIntegral geometry.
000711942 650_0 $$aGraph labelings.
000711942 7001_ $$aFu, Joseph H. G.,$$eauthor.
000711942 7001_ $$aGallego, Eduardo,$$eeditor.
000711942 7001_ $$aSolanes, Gil,$$eeditor.
000711942 830_0 $$aAdvanced courses in mathematics, CRM Barcelona.
000711942 85280 $$bebk$$hSpringerLink
000711942 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0874-3$$zOnline Access
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