Geometric Analysis on Real Analytic Manifolds

Lewis, Andrew D.

Geometric Analysis on Real Analytic Manifolds
  • 出版商: Springer
  • 出版日期: 2023-11-08
  • 售價: $2,750
  • 貴賓價: 9.5 折 $2,613
  • 語言: 英文
  • 頁數: 314
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031379128
  • ISBN-13: 9783031379123

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商品描述

This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings.

Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.

商品描述(中文翻譯)

這本專著提供了一些在實解析流形上進行全局幾何分析的有用工具。本書方法的核心是對實解析向量丛的實解析截面空間和實解析流形之間的實解析映射空間的拓撲進行多種描述。在這些拓撲的各種描述中，包括對實解析截面空間的幾何半范數的發展。為了說明本書中的技巧，展示了一些微分幾何中的基本構造如何在實解析截面和映射空間上引出連續映射。

本書針對博士研究生及以上的研究人員，介紹了實解析分析和幾何學的挑戰和機遇。

作者簡介

​Prof. Andrew Lewis received his Doctorate in Applied Mechanics in 1995 from the California Institute of Technology. From 1996-1998 he was a Postdoctoral Fellow in the Mathematics Institute at the University of Warwick. In 1998, he joined the Department of Mathematics and Statistics at Queen's University, and has remained there till the present. He became Associate Professor in 2004 and Full Professor in 2014.

He has published in the areas of geometric control theory, geometric mechanics, and geometric functional analysis. He has published three books: (1) Geometric Control of Mechanical Systems (with F. Bullo, Springer Texts in Applied Mathematics, 2004); (2) Time-Varying Vector Fields and Their Flows (with S. Jafarpoour, Springer Briefs in Mathematics, 2014); and (3) Tautological Control Systems (Springer Briefs in Control, 2014).

作者簡介(中文翻譯)

Prof. Andrew Lewis於1995年從加州理工學院獲得應用力學博士學位。從1996年至1998年，他在華威大學數學研究所擔任博士後研究員。1998年，他加入了女王大學數學與統計學系，並一直留在那裡至今。他於2004年成為副教授，並於2014年晉升為正教授。

他在幾何控制理論、幾何力學和幾何函數分析領域發表了多篇論文。他出版了三本書籍：(1)《機械系統的幾何控制》（與F. Bullo合著，Springer應用數學文本，2004年）；(2)《時變向量場及其流》（與S. Jafarpoour合著，Springer數學簡報，2014年）；以及(3)《自明控制系統》（Springer控制簡報，2014年）。

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