Overview
- Presents essential knowledge in a compact format
- Concentrates on the theoretical fundamentals relevant to applied mathematics
- Includes carefully chosen examples and exercises
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents (17 chapters)
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Front Matter
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Topological Basics
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Front Matter
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Linear Operators Between Normed Spaces
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Front Matter
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Dual Spaces and Weak Convergence
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Front Matter
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Compact Operators Between Banach Spaces
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Front Matter
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Hilbert Spaces
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Front Matter
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Keywords
About this book
Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing.
This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.
Reviews
“The first remarkable aspect of this unique book is its unifying approach. … The book also is well written, is self-contained, and includes timely, useful lists of references. Any researcher or graduate student working on fractional-in-time semilinear equations should read this essential book.” (Pablo Raúl Stinga, SIAM Review, Vol. 64 (1), March, 2022)
“In my next functional analysis course I will definitely include Clason’s book in my reading list … . this book is a valuable addition to the literature for anyone teaching a one-semester course in functional analysis. It covers all the important topics that we want graduate students to understand, and in a very structured and efficient way. Students may find it helpful to have an efficient and concise textbook for self-study and reference purposes.” (Armin Schikorra, SIAM Review, Vol. 63 (4), December, 2021)
“I do like the book! Most impressive to me is perhaps that the whole text is just 160 pages and still the explanations do not feel condensed while really the essential points are taken care of.” (Olav Nygaard, zbMATH 1461.46001, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Functional Analysis
Authors: Christian Clason
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-030-52784-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-52783-9Published: 01 December 2020
eBook ISBN: 978-3-030-52784-6Published: 30 November 2020
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: X, 170
Number of Illustrations: 1 b/w illustrations
Topics: Functional Analysis