# A Course in Functional Analysis and Measure Theory

Part of the Universitext book series (UTX)

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Textbook

Part of the Universitext book series (UTX)

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis.

Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory.

Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.

MSC (2010): 46-01, 47-01, 28-01 Lebesgue measure Lebesgue integral Hahn-Banach theorem Banach spaces closed graph theorem spectrum and eigenvalues Hilbert space self-adjoint operator fixed-point theorems locally convex spaces weak topology Krein-Milman theorem Lyapunov convexity theorem Fourier transform spectral measure

- DOI https://doi.org/10.1007/978-3-319-92004-7
- Copyright Information Springer International Publishing AG, part of Springer Nature 2018
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-92003-0
- Online ISBN 978-3-319-92004-7
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
- Buy this book on publisher's site