A Journey Through Ergodic Theorems
暫譯: 遍歷遍歷定理的旅程

Eisner, Tanja, Farkas, Bálint

A Journey Through Ergodic Theorems
  • 出版商: Birkhauser Boston
  • 出版日期: 2025-11-18
  • 售價: $3,570
  • 貴賓價: 9.5 折 $3,392
  • 語言: 英文
  • 頁數: 559
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031965051
  • ISBN-13: 9783031965050
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

The purpose of this book is to provide an invitation to the beautiful and important subject of ergodic theorems, both classical and modern, which lies at the intersection of many fundamental mathematical disciplines: dynamical systems, probability theory, topology, algebra, number theory, analysis and functional analysis. The book is suitable for undergraduate and graduate students as well as non-specialists with basic knowledge of functional analysis, topology and measure theory.

Starting from classical ergodic theorems due to von Neumann and Birkhoff, the state-of-the-art of modern ergodic theorems such as subsequential, multiple and weighted ergodic theorems are presented. In particular, two deep connections between ergodic theorems and number theory are discussed: Furstenberg's famous proof of Szemerédi's theorem on existence of arithmetic progressions in large sets of integers, and the Sarnak conjecture on the random behavior of the Möbius function.

An extensive list of references to other literature for readers wishing to deepen their knowledge is provided.

商品描述(中文翻譯)

本書的目的是邀請讀者探索美麗且重要的遍歷定理（ergodic theorems），包括古典與現代的遍歷定理，這一主題位於許多基本數學學科的交匯處：動態系統、機率論、拓撲學、代數、數論、分析學及泛函分析。本書適合本科生、研究生以及具備基本泛函分析、拓撲學和測度論知識的非專家讀者。

本書從冯·诺依曼（von Neumann）和比爾科夫（Birkhoff）提出的古典遍歷定理開始，介紹現代遍歷定理的最新進展，例如子序列遍歷定理、多重遍歷定理和加權遍歷定理。特別地，討論了遍歷定理與數論之間的兩個深刻聯繫：Furstenberg 對 Szemerédi 定理的著名證明，該定理關於在大整數集合中存在算術級數，以及 Sarnak 猜想，該猜想涉及 Möbius 函數的隨機行為。

本書提供了廣泛的參考文獻列表，供希望深入了解的讀者參考。

作者簡介

Tanja Eisner received her PhD at the University of Tübingen in 2007 and completed her habilitation in 2010. She moved in 2011 to the University of Amsterdam as assistant professor and since 2013 is a full professor at the University of Leipzig. In the meantime, she had research stays at the University of Missouri, Columbia, at the Paul Verlaine University, Metz and, repeatedly, at the University of California, Los Angeles. Her research focuses on operator theory, ergodic theory and connections with number theory. She is the author of the monograph "Stability of Operators and Operator Semigroups" published by Birkhäuser Verlag and a co-author, jointly with Bálint Farkas, Markus Haase and Rainer Nagel, of the book "Operator Theoretic Aspects of Ergodic Theory" published in the Springer Graduate Texts in Mathematics series. She is editor of the journals "Analysis Mathematica" and "Zeitschrift für Analysis und ihre Anwendungen" and is a former managing editor of the latter.

Bálint Farkas received his PhD from Eötvös Loránd University, Budapest, in 2004, with a stay at the Central European University and as a Marie Curie Fellow at the University of Tübingen during his PhD studies. Afterward, he worked as a postdoctoral researcher at the Alfréd Rényi Institute of Mathematics in Budapest, the University of Parma, and the University of Tübingen. He held faculty positions at the Technical University of Darmstadt and Eötvös Loránd University, Budapest. Since 2012, he has been a professor at the University of Wuppertal. His research focuses on functional analysis, operator theory, and their applications, particularly in dynamical systems. Together with Tanja Eisner, Markus Haase, and Rainer Nagel, he co-authored the book "Operator Theoretic Aspects of Ergodic Theory", which was published in the Springer Graduate Texts in Mathematics series. He serves as a deputy-editor-in-chief for the journal "Analysis Mathematica" and as an editor for "Zeitschrift für Analysis und ihre Anwendungen".

作者簡介(中文翻譯)

Tanja Eisner 於2007年在圖賓根大學獲得博士學位，並於2010年完成了資格論文。她於2011年轉至阿姆斯特丹大學擔任助理教授，自2013年起成為萊比錫大學的正教授。在此期間，她曾在密蘇里大學哥倫比亞分校、保羅·維爾萊大學（Paul Verlaine University, Metz）以及加州大學洛杉磯分校進行研究。她的研究專注於算子理論、遍歷理論及其與數論的聯繫。她是由Birkhäuser Verlag出版的專著《算子的穩定性與算子半群》（'Stability of Operators and Operator Semigroups'）的作者，並與Bálint Farkas、Markus Haase和Rainer Nagel共同合著了在Springer數學研究生系列中出版的書籍《遍歷理論的算子理論方面》（'Operator Theoretic Aspects of Ergodic Theory'）。她是期刊《數學分析》（'Analysis Mathematica'）和《分析及其應用期刊》（'Zeitschrift für Analysis und ihre Anwendungen'）的編輯，並曾擔任後者的主編。

Bálint Farkas 於2004年在布達佩斯厄爾特大學獲得博士學位，並在中央歐洲大學及圖賓根大學擔任瑪麗·居里研究員。在此之後，他在布達佩斯的阿爾弗雷德·雷尼數學研究所、帕爾馬大學和圖賓根大學擔任博士後研究員。他曾在達姆施塔特工業大學和布達佩斯厄爾特大學擔任教職。自2012年以來，他一直是伍珀塔爾大學的教授。他的研究專注於函數分析、算子理論及其應用，特別是在動態系統中的應用。與Tanja Eisner、Markus Haase和Rainer Nagel共同合著的書籍《遍歷理論的算子理論方面》（'Operator Theoretic Aspects of Ergodic Theory'）已在Springer數學研究生系列中出版。他擔任期刊《數學分析》（'Analysis Mathematica'）的副主編，並擔任《分析及其應用期刊》（'Zeitschrift für Analysis und ihre Anwendungen'）的編輯。

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