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Integral Geometry and Valuations / by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes
(Advanced Courses in Mathematics - CRM Barcelona. ISSN:22970312)
版 | 1st ed. 2014. |
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出版者 | Basel : Springer Basel : Imprint: Birkhäuser |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | VIII, 112 p : online resource |
著者標目 | *Alesker, Semyon author Fu, Joseph H.G author Gallego, Eduardo editor Solanes, Gil editor SpringerLink (Online service) |
件 名 | LCSH:Convex geometry LCSH:Discrete geometry LCSH:Geometry, Differential FREE:Convex and Discrete Geometry FREE:Differential Geometry |
一般注記 | Part 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 Valuations 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-0874-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783034808743 |
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EB00233569 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA639.5-640.7 LCC:QA640.7-640.77 DC23:516 |
書誌ID | 4000119409 |
ISBN | 9783034808743 |
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※2017年9月4日以降