Harmonic Analysis and Partial Differential Equations
Harmonic Analysis and Partial Differential Equations
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DOI：
10.1007/978-3-031-24311-0
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Cameron Gordon
中科院分区：
文献类型：
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作者：
Cameron Gordon
本书是根据法国École Normale supsamrieure（巴黎高等师范学院和巴黎萨克雷高等师范学院）和清华大学先后开设的几门不同课程的笔记编写的。我没有在这本书中添加任何没有教过的东西，书中出现的所有证明都写在了黑板上。我试图为研究生课程提供一个要求严格但又容易理解的说明。全书共分为五个部分，内容如下。它的目的是给一个完全沉浸在数学分析的先进概念，围绕四个领域，涵盖泛函分析，谐波分析，微局部分析和偏微分方程的分析。每一章都是为读者提供基本概念的理解，同时指导他们通过一些重要定理的详细证明。
This book is based on the notes from several different courses given successively at the École Normale Supérieure in France (ENS Paris and ENS Paris-Saclay) and at Tsinghua University. I have added nothing in this book that was not taught, and all the proofs that appear in this book were written on the board. I have tried to offer a demanding but nevertheless accessible exposition of graduate courses. The book is divided into five parts, whose contents are described below. It aims to give a complete immersion in the advanced concepts of Mathematical Analysis and revolves around four domains, covering Functional Analysis, Harmonic Analysis, Microlocal Analysis, and the Analysis of Partial Differential Equations. Each chapter is constructed to provide readers with an understanding of fundamental concepts while guiding them through the detailed proofs of some significant theorems.