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特征值.不等式和遍歷理論-(影印版) 版權信息
- ISBN：9787510052675
- 條形碼：9787510052675 ; 978-7-5100-5267-5
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
特征值.不等式和遍歷理論-(影印版) 本書特色
陳木法編著的《特征值、不等式和遍歷理論》詳細講述了應用廣泛眾多讀者感興趣的問題———矩陣的譜隙和微分算子，提供了描述相變換和隨機算術效應的工具。每章以綜述開始，為了吸引更多的非專業人士，通過簡單例子引入觀點而不是技巧證明。后面的一些章節很自然地將讀者引入這個領域的問題和應用中，如經濟的隨機模型等。 讀者對象：數學、統計、經濟領域的學生和相關的科研人員。
特征值.不等式和遍歷理論-(影印版) 內容簡介
this book surveys， in a popular way， the main progress made in the field by our group. it consists of ten chapters plus two appendixes. the first chapter is an overview of the second to the eighth ones. mainly， we study several different inequalities or different types of convergence by using three mathematical tools: a probabilistic tool， the coupling methods （chapters 2 and 3）; a generalized cheeger's method originating in riemannian geometry （chapter 4）; and an approach coming from potential theory and harmonic analysis （chapters 6 and 7）. the explicit criteria for different types of convergence and the explicit estimates of the convergence rates （or the optimal constants in the inequalities） in dimension one are given in chapters 5 and 6; some generalizations are given in chapter 7. the proofs of a diagram of nine types of ergodicity （theorem 1.9） are presented in chapter 8.
特征值.不等式和遍歷理論-(影印版) 目錄
preface
acknowledgments
chapter 1 an overview of the book
1.1 introduction
1.2 new variational formula for the first eigenvalue
1.3 basic inequalities and new forms of cheeger's constants
1.4 a new picture of ergodic theory and explicit criteria
chapter 2 optimal markovian couplings
2.1 couplings and markovian couplings
2.2 optimality with respect to distances
2.3 optimality with respect to closed functions
2.4 applications of coupling methods
chapter 3 new variational formulas for the first eigenvalue
3.1 background
3.2 partial proof in the discrete case
acknowledgments
chapter 1 an overview of the book
1.1 introduction
1.2 new variational formula for the first eigenvalue
1.3 basic inequalities and new forms of cheeger's constants
1.4 a new picture of ergodic theory and explicit criteria
chapter 2 optimal markovian couplings
2.1 couplings and markovian couplings
2.2 optimality with respect to distances
2.3 optimality with respect to closed functions
2.4 applications of coupling methods
chapter 3 new variational formulas for the first eigenvalue
3.1 background
3.2 partial proof in the discrete case
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特征值.不等式和遍歷理論-(影印版) 作者簡介
陳木法是中科院院士，國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。
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