Tools for Infinite Dimensional Analysis
暫譯: 無限維分析工具

Becnel, Jeremy J.

Tools for Infinite Dimensional Analysis
  • 出版商: CRC
  • 出版日期: 2020-12-29
  • 售價: $6,820
  • 貴賓價: 9.5 折 $6,479
  • 語言: 英文
  • 頁數: 274
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367543664
  • ISBN-13: 9780367543662

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

Over the past six decades, several extremely important fields in mathematics have been developed. Among these are It calculus, Gaussian measures on Banach spaces, Malliavan calculus, and white noise distribution theory. These subjects have many applications, ranging from finance and economics to physics and biology.

Unfortunately, the background information required to conduct research in these subjects presents a tremendous roadblock. The background material primarily stems from an abstract subject known as infinite dimensional topological vector spaces. While this information forms the backdrop for these subjects, the books and papers written about topological vector spaces were never truly written for researchers studying infinite dimensional analysis. Thus, the literature for topological vector spaces is dense and difficult to digest, much of it being written prior to the 1960s.

Tools for Infinite Dimensional Analysis aims to address these problems by providing an introduction to the background material for infinite dimensional analysis that is friendly in style and accessible to graduate students and researchers studying the above-mentioned subjects. It will save current and future researchers countless hours and promote research in these areas by removing an obstacle in the path to beginning study in areas of infinite dimensional analysis.

Features

  • Focused approach to the subject matter

  • Suitable for graduate students as well as researchers

  • Detailed proofs of primary results

商品描述(中文翻譯)

在過去六十年中，數學領域發展了幾個極為重要的領域。其中包括 It 微積分、在 Banach 空間上的高斯測度、Malliavan 微積分以及白噪聲分佈理論。這些主題有許多應用，涵蓋了金融、經濟學、物理學和生物學等領域。

不幸的是，進行這些主題研究所需的背景知識構成了一個巨大的障礙。這些背景材料主要源自一個抽象的主題，稱為無限維拓撲向量空間。雖然這些信息為這些主題提供了背景，但有關拓撲向量空間的書籍和論文從未真正為研究無限維分析的研究人員而寫。因此，拓撲向量空間的文獻密集且難以消化，其中許多作品是在1960年代之前撰寫的。

《無限維分析工具》旨在通過提供無限維分析背景材料的介紹，來解決這些問題，該介紹風格友好，適合研究上述主題的研究生和研究人員。它將為當前和未來的研究人員節省無數小時，並通過消除進入無限維分析領域學習的障礙，促進這些領域的研究。

特點
- 專注於主題內容
- 適合研究生及研究人員
- 主要結果的詳細證明

作者簡介

Jeremy J. Becnel was born in the rural community of Kraemer, Louisiana, in 1979 and completed his undergraduate studies in mathematics and computer science at Nicholls State University in May 2001. He earned a Master of Science degree from Louisiana State University in December 2002 and a PhD in August 2006. Immediately after graduation, Dr. Becnel began working at Stephen F. Austin State University (SFASU). He has worked at SFASU for fifteen years as a professor in the Department of Mathematics and the Department of Computer Science. During this time, Dr. Becnel has supervised numerous undergraduate research projects and graduate theses. He is a recipient of the National Science Foundation Division of Undergraduate Research grant and a Young Investigator's Grant from the National Security Agency, among others. Through the former grant, he has worked with colleagues to create CalcVR, a virtual reality app for multivariable calculus. His research interests include quantum computing, Radon transforms, probability theory, white noise analysis, and topological vector spaces. 　Dr. Becnel currently lives in the small town of Nacogdoches, Texas with his wife, Kesha, along with their daughters, Alyssa and Anna.

作者簡介(中文翻譯)

Jeremy J. Becnel 於1979年出生於路易斯安那州的克雷默（Kraemer）農村社區，並於2001年5月在尼科爾斯州立大學（Nicholls State University）完成數學和計算機科學的本科學位。他於2002年12月獲得路易斯安那州立大學（Louisiana State University）的理學碩士學位，並於2006年8月獲得博士學位。畢業後，Becnel博士立即開始在史蒂芬·F·奧斯丁州立大學（Stephen F. Austin State University, SFASU）工作。他在SFASU擔任數學系和計算機科學系的教授已有十五年。在此期間，Becnel博士指導了許多本科研究項目和研究生論文。他是美國國家科學基金會（National Science Foundation）本科研究部門的資助獲得者，以及國家安全局（National Security Agency）的青年研究者獎學金獲得者等。通過前者的資助，他與同事合作創建了CalcVR，一個用於多變量微積分的虛擬現實應用程式。他的研究興趣包括量子計算、拉東變換（Radon transforms）、概率論、白噪聲分析和拓撲向量空間。　Becnel博士目前與妻子Kesha及女兒Alyssa和Anna居住在德克薩斯州的小鎮納科多奇斯（Nacogdoches）。

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