Authors:
- Provides necessary preliminaries
- Explores basic and advanced material in functional analysis and operator theory, including applications to Fourier series and the Fourier transform
- Includes over 1500 exercises
Part of the book series: Universitext (UTX)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- 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
Reviews
Authors and Affiliations
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School of Mathematics and Computer Science, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
Vladimir Kadets
About the author
Vladimir Kadets has authored two monographs and more than 100 articles in peer-reviewed journals, mainly in Banach space theory: sequences and series, bases, vector-valued measures and integration, measurable multi-functions and selectors, isomorphic and isometric structures of Banach spaces, operator theory. In 2005 he received the State Award of Ukraine in Science and Technology to honour his research. The present book reflects the author’s teaching experience in the field, spanning over more than 20 years.
Bibliographic Information
Book Title: A Course in Functional Analysis and Measure Theory
Authors: Vladimir Kadets
Translated by: Andrei Iacob
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-92004-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-92003-0Published: 20 July 2018
eBook ISBN: 978-3-319-92004-7Published: 10 July 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXII, 539
Additional Information: Original Russian edition published by V.N. Karazin Kharkiv National University, Kharkiv, 2006
Topics: Functional Analysis, Measure and Integration, Operator Theory, Real Functions