Overview
- Presents the principles of functional analysis in a clear and concise way
- Most competing titles are out of date
- Includes very recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis ?
Part of the book series: Cornerstones (COR)
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Table of contents (10 chapters)
Keywords
About this book
The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics.
Reviews
From the reviews:
“The book is a very good contribution to the literature in a classical field of analysis. It should be of interest to specialists in pure and applied functional analysis and it can be used by advanced graduate students whom it will bring to the forefront of research. The book also serves to prepare the student for more advanced topics in analysis, especially the modern theory of partial differential equations.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1284, 2014)
Authors and Affiliations
Bibliographic Information
Book Title: Functional Analysis
Book Subtitle: Fundamentals and Applications
Authors: Michel Willem
Series Title: Cornerstones
DOI: https://doi.org/10.1007/978-1-4614-7004-5
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2013
Softcover ISBN: 978-1-4899-8794-5Published: 23 August 2015
eBook ISBN: 978-1-4614-7004-5Published: 13 August 2013
Series ISSN: 2197-182X
Series E-ISSN: 2197-1838
Edition Number: 1
Number of Pages: XIII, 213
Number of Illustrations: 18 b/w illustrations
Topics: Functional Analysis, Analysis, Partial Differential Equations, Mathematics, general