數學經典教材：經典位勢論及其對應的概率論（影印版）（英文版） [Classical Potential Theory and Its Probabilistic Counterpart] epub pdf mobi txt 電子書 下載 2024

數學經典教材：經典位勢論及其對應的概率論（影印版）（英文版） [Classical Potential Theory and Its Probabilistic Counterpart] epub pdf mobi txt 電子書 下載 2024

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數學經典教材：經典位勢論及其對應的概率論（影印版）（英文版） [Classical Potential Theory and Its Probabilistic Counterpart] epub pdf mobi txt 電子書 下載 2024

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內容簡介

　　Potential theory and certain aspects of probability theory are intimately related， perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically， a procedure potential theorists observe with jaun- diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory， specifically to concepts in martingale theory.For example， superharmonic functions correspond to supermartingales. More specifically： the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super- martingales; certain positive superharmonic functions [supermartingales] are called "potentials，" have associated measures in their respective theories and are subject to domination principles （inequalities） invomng the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping （balayage） of the measures associated with potentials， and，so on.

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目錄

Introduction
Notation and Conventions
Part 1
Classical and Parabolic Potential Theory
Chapter I
Introduction to the Mathematical Background of Classical Potential Theory
1.The Context of Green's Identity
2.Function Averages
3.Harmonic Functions
4.Maximum-Minimum Theorem for Harmonic Functions
5.The Fundamental Kernel for RN and Its Potentials
6.Gauss Integral Theorem
7.The Smoothness of Potentials ; The Poisson Equation
8.Harmonic Measure and the Riesz Decomposition
Chapter II
Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions
1.The Green Function of a Ball; The Poisson Integral
2.Hamack's Inequality
3.Convergence of Directed Sets of Harmonic Functions
4.Harmonic, Subharmonic, and Superharmoruc Functions
5.Minimum Theorem for Superharmonic Functions
6.Application of the Operation TB
7.Characterization of Superharmonic Functions in Terms of Harmonic Functions
8.Differentiable Superharmonic Functions
9.Application of Jensen's Inequality
10.Superharmonic Funaions on an Annulus
II.Examples
12.The Kelvin Transformation
13.Greenian Sets
14.The L1（uB_） and D（uB_） Classes of Harmonic Functions on a Ball B; The
Riesz-Herglotz Theorem
15.The Fatou Boundary Limit Theorem
16.Minimal Harmonic Functions
Chapter III
Infima of Families of Superharmonic Functidns
1.Least Superharmonic Majorant （LM） and Greatest Subharmonic Minorant （GM）
2.Generalization of Theorem I
3.Fundamental Convergence Theorem （Preliminary Version）
4.The Reduction Operation
5.Reduction Properties
6.A Smallness Property of Reductions on Compact Sets
7.The Natural （Pointwise） Order Decomposition for Positive Superharmonk
Functions
Chapter 1V
Potentials on Special Open Sets
1.Special Open Sets, and Potentials on Them
2.Examples
3.A Fundamental Smallness Property of Potentials
4.Increasing Sequences of Potentials
5.Smoothing of a Potential
6.Uniqueness of the Measure Determining a Potential
7.Riesz Measure Associated with a Superharmonic Function
8.Riesz Decomposition Theorem
9.Counterpart for Superharmonic Functions on R2 ofthe Riesz
Decomposition
10.An Approximation Theorem
Chapter V
Polar Sets and Their Applications
1.Definition
2.Superharmonic Functions Associated with a Polar Set
3.Countable Unions of Polar Sets
4.Properties ofPolar Sets
5.Extension of a Superharmonic Function
6.Greenian Sets in IR2 as the Complements of Nonpolar Sets
7.Superharmonic Function Minimum Theorem （Extension of Theorem I1.5）
8.Evans-Vasilesco Theorem
9.Approximation of a Potential by Continuous Potentials
10.The Domination Principle
I1.The Infinity Set of a Potential and the Riesz Measure
……

Part 2
Probabilistic Countrepart of Part 1
Part 3

數學經典教材：經典位勢論及其對應的概率論（影印版）（英文版） [Classical Potential Theory and Its Probabilistic Counterpart] epub pdf mobi txt 電子書 下載 2024

數學經典教材：經典位勢論及其對應的概率論（影印版）（英文版） [Classical Potential Theory and Its Probabilistic Counterpart] 下載 epub mobi pdf txt 電子書

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評分☆☆☆☆☆

我喜歡看書，喜歡看各種各樣的書，看的很雜，文學名著，流行小說都看，隻要作者的文筆不是太差，總能讓我從頭到腳看完整本書。隻不過很多時候是當成故事來看，看完瞭感嘆一番也就丟下瞭。所在來這裏買書是非常明智的。然而，目前社會上還有許多人被一些價值不大的東西所束縛，卻自得其樂，還覺得很滿足。經過幾百年的探索和發展，人們對物質需求已不再迫切，但對於精神自由的需求卻無端被抹殺瞭。總之，我認為現代人最缺乏的就是一種開闊進取，尋找最大自由的精神。中國人講虛實相生，天人閤一的思想，於空寂處見流行，於流行處見空寂，從而獲得對於道的體悟，唯道集虛。這在傳統的藝術中得到瞭充分的體現，

类似图書 點擊查看全場最低價