Authors:
- Second edition features new and expanded coverage of distribution theory and calculus, as well as other improvements
- Presents the principles of functional analysis in a clear and concise way
- Provides 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)
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Front Matter
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Back Matter
About this book
This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: 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 to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics.
The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.
Authors and Affiliations
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Department of Mathematics, Université catholique de Louvain, Louvain-la-Neuve, Belgium
Michel Willem
About the author
Bibliographic Information
Book Title: Functional Analysis
Book Subtitle: Fundamentals and Applications
Authors: Michel Willem
Series Title: Cornerstones
DOI: https://doi.org/10.1007/978-3-031-09149-0
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: 978-3-031-09148-3Published: 28 January 2023
Softcover ISBN: 978-3-031-09151-3Published: 28 January 2024
eBook ISBN: 978-3-031-09149-0Published: 27 January 2023
Series ISSN: 2197-182X
Series E-ISSN: 2197-1838
Edition Number: 2
Number of Pages: XV, 251
Number of Illustrations: 3 b/w illustrations
Topics: Functional Analysis