Overview
- Presents a set of the most relevant tools of modern analysis
- Covers the foundations of modern analysis in a compact and didactic way
- Gives young researchers all the techniques they need to explore this broad subject
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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Table of contents (8 chapters)
Keywords
About this book
Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis.
Eachchapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume.
By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Reviews
“I recommend this text as a standalone text for any student who is trying to learn this material for the first time. … I conjecture that, once paired, the two-volume set will make an excellent tool for researchers looking to quickly gain insight into the tools used in modern analytical research.” (John Ross, MAA Reviews, June 17, 2023)
Authors and Affiliations
About the authors
Nikolaos S. Papageorgiou is a Professor at the National Technical University of Athens, Greece. He holds a PhD in Applied Mathematics (1983) from Harvard University, USA, and degrees in Mathematics and Electrical Engineering, both from Massachusetts Institute of Technology – MIT. Dr. Papageorgiou has co-authored over a dozen books, including “Exercises in Analysis” (2016) and “Nonlinear Analysis - Theory and Methods” (2019), both published by Springer.
Bibliographic Information
Book Title: Research Topics in Analysis, Volume I
Book Subtitle: Grounding Theory
Authors: Shouchuan Hu, Nikolaos S. Papageorgiou
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-031-17837-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-17836-8Published: 30 November 2022
Softcover ISBN: 978-3-031-17839-9Published: 30 November 2023
eBook ISBN: 978-3-031-17837-5Published: 29 November 2022
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: XIII, 535
Topics: Functional Analysis, Topology, Optimization