Measure-Theoretic Calculus in Abstract Spaces: On the Playground of Infinite-Dimensional Spaces

Pan, Zigang

Measure-Theoretic Calculus in Abstract Spaces: On the Playground of Infinite-Dimensional Spaces
  • 出版商: Birkhauser Boston
  • 出版日期: 2024-01-24
  • 售價: $8,630
  • 貴賓價: 9.5 折 $8,199
  • 語言: 英文
  • 頁數: 933
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031219112
  • ISBN-13: 9783031219115
  • 相關分類: 微積分 Calculus

    • 下單後立即進貨 (約1週~2週)

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商品描述

This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The result of many years of the author's careful and extensive work, this text synthesizes and builds upon the existing literature in an effort to develop and solidify the theory of measure-theoretic calculus in abstract spaces. Standard results and proofs are illustrated in general abstract settings under rigorous treatment, and numerous ancillary topics are also covered in detail, such as functional analytic treatment of optimization, probability theory, and the theory of Sobolev spaces. Applied mathematicians and researchers working in control theory, operations research, economics, optimization theory, and many other areas will find this text to be a comprehensive and invaluable resource. It can also serve as an analysis textbook for graduate-level students.

商品描述(中文翻譯)

這本專著嚴謹地、百科全書式地介紹了實分析、泛函分析和測度論的基本主題。作者經過多年的細心和廣泛的工作，將現有文獻綜合並建立起來，以發展和鞏固抽象空間中的測度論微積分理論。標準結果和證明在嚴謹的處理下以一般抽象的設定來說明，並且還詳細介紹了許多相關主題，如最佳化的泛函分析處理、概率論和Sobolev空間理論。應用數學家和在控制理論、運籌學、經濟學、最佳化理論等領域工作的研究人員將會發現這本書是一個全面且寶貴的資源。它也可以作為研究生級別學生的分析教材。

作者簡介

Zigang Pan was born in 1968 in Shanghai, China. He received his B.S. degree in Automatic Control from Shanghai Jiao Tong University in 1990, and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Illinois at Urbana-Champaign in 1992 and 1996, respectively. In 1996, he was a Research Engineer at the Center for Control Engineering and Computation at the University of California, Santa Barbara. In the same year, he joined the Polytechnic University, Brooklyn, NY, (now the Tandon School of Engineering at the New York University) as an Assistant Professor in the Department of Electrical Engineering for two years. Afterwards, he joined the faculty of Shanghai Jiao Tong University, Shanghai, P. R. China, in the Department of Automation. In January 2001, he joined the Department of Electrical and Computer Engineering and Computer Science of the University of Cincinnati as an Assistant Professor. Since 2005, he is pursuing research on hisown interest.
His current research interest lie in optimality-guided robust adaptive control for single-input and single-output linear systems, and its generalization to multiple-input and multiple-output systems, as well as nonlinear systems. To solidify his background knowledge in mathematics for the control theory research, he has been working on this book for sixteen years.
He was a co-winner of the 1995 George Axelby Best Paper Award of the IEEE Transaction on Automatic Control together with Professor Tamer Başar of the University of Illinois at Urbana-Champaign. He was a Silver prize winner in the 28th International Mathematical Olympiad. He is a member of the IEEE and the AMS and an affiliate of IFAC.

作者簡介(中文翻譯)

潘子剛於1968年出生於中國上海。他於1990年獲得上海交通大學自動控制專業的學士學位，並於1992年和1996年分別獲得伊利諾伊大學香檳分校電機工程專業的碩士和博士學位。1996年，他在加州大學聖塔芭芭拉分校的控制工程和計算中心擔任研究工程師。同年，他加入了布魯克林的理工學院（現紐約大學坦頓工程學院）電機工程系擔任助理教授，任職兩年。之後，他加入了上海交通大學自動化系的教職。2001年1月，他加入辛辛那提大學電機與計算機工程學系擔任助理教授。自2005年以來，他一直在追求自己的研究興趣。
他目前的研究興趣主要集中在單輸入單輸出線性系統的最優引導魯棒自適應控制，以及其在多輸入多輸出系統和非線性系統中的推廣。為了鞏固他在控制理論研究中的數學背景知識，他已經致力於撰寫這本書已有十六年之久。
他曾與伊利諾伊大學香檳分校的塔默·巴薩爾教授共同獲得1995年IEEE自動控制交易的喬治·阿克塞爾比最佳論文獎。他還是第28屆國際數學奧林匹克銀獎得主。他是IEEE和AMS的成員，也是IFAC的聯繫人。

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