Introduction to Modern Analysis (Oxford Graduate Texts in Mathematics) (Paperback)
暫譯: 現代分析導論（牛津研究生數學系列）(平裝本)
Shmuel Kantorovitz
- 出版商: Oxford University
- 出版日期: 2006-08-24
- 售價: $1,180
- 貴賓價: 9.8 折 $1,156
- 語言: 英文
- 頁數: 448
- 裝訂: Paperback
- ISBN: 0199203156
- ISBN-13: 9780199203154
-
相關分類:
數值分析 Numerical-analysis、機率統計學 Probability-and-statistics
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商品描述
Description
This text is based on lectures given by the author at the advanced undergaraduate and graduate levels in Measure theory, Functional Analysis, Bannach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis and contain over 120 end of chapter exercises. the final two chapters apply theory to applications in Probability Theory and Partial Differential Equations.
Table of Contents
Preface1. Measures2. Construction of measures3. Measure and topology4. Continuous linear functionals5. Duality6. Bounded operators7. Banach algebras8. Hilbert spaces9. Integral representation10. Unbounded operatorsApplication I:ProbabilityApplication II: DistributionsBibliographyIndex
商品描述(中文翻譯)
**描述**
本書內容基於作者在高級本科及研究生層級的講座，涵蓋測度論、泛函分析、巴拿赫代數、譜理論（有界及無界算子）、算子半群、概率與數理統計以及偏微分方程。前十章討論測度論和泛函分析中的理論方法，並包含超過120個章末練習題。最後兩章將理論應用於概率論和偏微分方程的實際應用。
**目錄**
- 前言
- 1. 測度
- 2. 測度的構造
- 3. 測度與拓撲
- 4. 連續線性泛函
- 5. 對偶性
- 6. 有界算子
- 7. 巴拿赫代數
- 8. 希爾伯特空間
- 9. 積分表示
- 10. 無界算子
- 應用 I: 概率
- 應用 II: 分佈
- 參考文獻
- 索引
