不等式(英文) [Inequalities:A Journey into Linear Analysis]

不等式(英文) [Inequalities:A Journey into Linear Analysis] 下載 mobi epub pdf 電子書 2024


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[英] 加林(Garling D.J.H.) 著



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圖書介紹

齣版社: 世界圖書齣版公司
ISBN:9787510042829
版次:1
商品編碼:10975217
包裝:平裝
外文名稱:Inequalities:A Journey into Linear Analysis
開本:16開
齣版時間:2012-03-01
用紙:膠版紙
頁數:335
正文語種:英文


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內容簡介

Thus there are very many important inequalities.This book is not intended to be a compendium of these; instead, it provides an introduction to a selection of inequalities, not including any of those mentioned above. The inequalities that we consider have a common theme; they relate to problems in real analysis, and more particularly to problems in real analysis. Incidentally, they include many of the inequalities considered in the fascinating and ground-breaking book Inequalities,by Hardy, Littlewood and Polya, originally published in 1934.

內頁插圖

目錄

Introduction
1 Measure and integral
1.1 Measure
1.2 Measurable functions
1.3 Integration
1.4 Notes and remarks

2 The Cauchy-Schwarz inequality
2.1 Cauchy's inequality
2.2 Inner-product spaces
2.3 The Cauchy-Schwarz inequality
2.4 Notes and remarks
3 The AM-GM inequality
3.1 The AM-GM inequality
3.2 Applications
3.3 Notes and remarks

4 Convexity and Jensen's inequality
4.1 Convex sets and convex functions
4.2 Convex functions on an interval
4.3 Directional derivatives and sublinear functionals
4.4 The Hahn-Banach theorem
4.5 Normed spaces, Banach spaces and Hilbert space
4.6 The Hahn-Banach theorem for normed spaces
4.7 Barycentres and weak integrals
4.8 Notes and remarks

5 The Lp spaces
5.1 Lp spaces, and Minkowski's inequality
5.2 The Lebesgue decomposition theorem
5.3 The reverse Minkowski inequality
5.4 HSlder's inequality
5.5 The inequalities of Liapounov and Littlewood
5.6 Duality
5.7 The Loomis-Whitney inequali'ty
5.8 A Sobolev inequality
5.9 Schur's theorem and Schur's test
5.10 Hilbert's absolute inequality
5.11 Notes and remarks

6 Banach function spaces
6.1 Banach function spaces
6.2 Function space duality
6.3 Orlicz space
6.4 Notes and remarks

7 Rearrangements
7.1 Decreasing rearrangements
7.2 Rearrangement-invariant Banach function spaces
7.3 Muirhead's maximal function
7.4 Majorization
7.5 Calder6n's interpolation theorem and its converse
7.6 Symmetric Banach sequence spaces
7.7 The method of transference
7.8 Finite doubly stochastic matrices
7.9 Schur convexity
7.10 Notes and remarks Maximal inequalities

8.1 The Hardy-Riesz inequality
8.2 The Hardy-Riesz inequality
8.3 Related inequalities
8.4 Strong type and weak type
8.5 Riesz weak type
8.6 Hardy, Littlewood, and a batsman's averages
8.7 Riesz's sunrise lemma
8.8 Differentiation almost everywhere
8.9 Maximal operators in higher dimensions
8.10 The Lebesgue density theorem
8.11 Convolution kernels
8.12 Hedberg's inequality
……
9 Complex interpolation
10 Real interpolation
11 The Hilbert transform, and Hilbert's inequalities
12 Khintchine's inequality
13 Hypercontractive and logarithmic Sobolev inequalities
14 Hadamard's inequality
15 Hilbert space operator inequalities
16 Summing operators
17 Approximation numbers and eigenvalues
18 Grothendieck's inequality, type and cotype
References
Index of inequalities
Index

前言/序言



不等式(英文) [Inequalities:A Journey into Linear Analysis] 下載 mobi epub pdf txt 電子書 格式

不等式(英文) [Inequalities:A Journey into Linear Analysis] mobi 下載 pdf 下載 pub 下載 txt 電子書 下載 2024

不等式(英文) [Inequalities:A Journey into Linear Analysis] 下載 mobi pdf epub txt 電子書 格式 2024

不等式(英文) [Inequalities:A Journey into Linear Analysis] 下載 mobi epub pdf 電子書
想要找書就要到 圖書大百科
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

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