漸近幾何分析 (第Ⅰ部分) (英文) 希里.阿特斯坦-阿維丹 9787040612578 【台灣高等教育出版社】
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物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：漸近幾何分析 (第Ⅰ部分) (英文) ISBN：9787040612578 出版社：高等教育 著編譯者：希里.阿特斯坦-阿維丹 頁數：451 所在地：中國大陸 *此為代購商品 書號：1625183 可大量預訂，請先連絡。 內容簡介 作者簡介 了漸近幾何分析理論，這是一個介於幾何學與泛函分析之間的領域。在這個領域中，「同構」的觀點取代了低維幾何的典型等距問題，並引入了漸近方法（當維數趨於無窮時）。幾何和分析在這裏以一種非平凡的方式相遇。書中遇到的同構形式幾何不等式的基本例子是「同構等距不等式」，它導致了「集中現象」的發現，這是該理論最強大的工具之一，由此得到了許多反直覺的結果。 本書的核心主題是隨機性和模式的相互作用。乍一看，高維的生命似乎意味著存在多種「可能性」，因此人們可以預期，隨著維度的增加，多樣性和複雜性也會增加。然而，測量的集中和由凸性引起的效應表明，對於由高維引起的混合體中的任意凸體，這種多樣性得到了補償，並且產生了秩序和模式。 本書面向想要了解這個令人興奮的主題的研究生和研究人員。書中涵蓋的主題包括凸性、集中現象、覆蓋數、Dvoretzky型定理、凸體中的體積分佈等。目錄 PrefaceChapter 1 Convex bodies: classical geometric inequalities 1 1 Basic convexity 1 2 Brunn-Minkowski inequality 1 3 Volume preserving transformations 1 4 Functional forms 1 5 Applications of the Brunn-Minkowski inequality 1 6 Minkowski's problem 1 7 Notes and remarks Chapter 2 Classical positions of convex bodies 2 1 John's theorem 2 2 Minimal mean width position 2 3 Minimal surface area position 2 4 Reverse isoperimetric inequality 2 5 Notes and remarks Chapter 3 Isomorphic isoperimetric inequalities and concentration of measure 3 1 An approach through extremal sets， and the basic terminology 3 2 Deviation inequalities for Lipschitz functions on classical metric probability spaces 3 3 Concentration on homogeneous spaces 3 4 An approach through conditional expectation and martingales 3 5 Khintchine type inequalities 3 6 Raz's Lemma 3 7 Notes and remarks Chapter 4 Metric entropy and covering numbers estimates 4 1 Covering numbers 4 2 Sudakov's inequality and its dual 4 3 Entropy numbers and approximation numbers 4 4 Duality of entropy 4 5 Notes and remarks Chapter 5 Almost Euclidean subspaces of finite dimensional normed spaces 5 1 Dvoretzky type theorems 5 2 Milman's proof 5 3 The critical dimension k(X) 5 4 Euclidean subspaees of gp 5 5 Volume ratio and Kashin's theorem 5 6 Global form of the Dvoretzky-Milman theorem 5 7 Isomorphic phase transitions and thresholds 5 8 Small ball estimates 5 9 Dependence on E 5 10 Notes and remarks Chapter 6 The g-position and the Rademacher projection 6 1 Hermite polynomials 6 2 Pisier's inequality 6 3 The Rademacher projection 6 4 The l-norm 6 5 The MM*-estimate 6 6 Equivalence of the two projections 6 7 Bourgain's example 6 8 Notes and remarks Chapter 7 Proportional Theory 7 1 Introduction 7 2 First proofs of the M*-estimate 7 3 Proofs with the optimal dependence 7 4 Milman's quotient of subspace theorem 7 5 Asymptotic formulas for random sections 7 6 Linear duality relations 7 7 Notes and remarks Chapter 8 M-position and the reverse Brunn-Minkowski inequality 8 1 Introduction 8 2 The Bourgain-Milman inequality 8 3 Isomorphic symmetrization 8 4 Milman's reverse Brunn-Minkowski inequality 8 5 Extension to the non-symmetric case 8 6 Applications of the M-position 8 7 α-regular M-position: Pisier's approach 8 8 Notes and remarks Chapter 9 Ganssian approach 9 1 Dudley， and another look at Sudakov 9 2 Gaussian proof of Dvoretzky theorem 9 3 Gaussian proof of the M*-estimate 9 4 Random orthogonal factorizations 9 5 Comparison principles for Gaussian processes 9 6 Notes and remarks Chapter 10 Volume distribution in convex bodies 10 1 Isotropic position 10 2 Isotropic log-concave measures 10 3 Bourgain's upper bound for the isotropic constant 10 4 Paouris' deviation inequality 10 5 The isomorphic slicing problem 10 6 A few technical inequalities for log-concave functions 10 7 Notes and remarks Appendix A Elementary convexity A 1 Basic convexity A 2 Convex functions A 3 Hausdorff distance A 4 Compactness: Blaschke's selection theorem A 5 Steiner symmetrization properties in detail A 6 Notes and remarks Appendix B Advanced convexity B 1 Mixed volumes B 2 The Alexandrov-Fenchel inequality B 3 More geometric inequalities of "hyperbolic" type B 4 Positive definite matrices and mixed discriminants B 5 Steiner's formula and Kubota's formulae B 6 Notes and remarks Bibliography Subject Index Author Index 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
