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A Course in Functional Analysis and Measure Theory de Vladimir Kadets

A Course in Functional Analysis and Measure Theory: Universitext

Autor Vladimir Kadets Traducere de Andrei Iacob
en Limba Engleză Paperback – 20 iul 2018
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.
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Specificații

ISBN-13: 9783319920030
ISBN-10: 3319920030
Pagini: 543
Ilustrații: XXII, 539 p.
Dimensiuni: 155 x 235 x 37 mm
Greutate: 0.78 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

Introduction.- Chapter 1. Metric and topological spaces.- Chapter 2. Measure theory.- Chapter 3. Measurable functions.- Chapter 4. The Lebesgue integral.- Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem.- Chapter 6. Normed spaces.- Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral.- Chapter 8. The integral on C(K).- Chapter 9. Continuous linear functionals.- Chapter 10. Classical theorems on continuous operators.- Chapter 11. Elements of spectral theory of operators. Compact operators.- Chapter 12. Hilbert spaces.- Chapter 13. Functions of an operator.- Chapter 14. Operators in Lp.- Chapter 15. Fixed-point theorems and applications.- Chapter 16. Topological vector spaces.- Chapter 17. Elements of duality theory.- Chapter 18. The Krein-Milman theorem and applications.- References. Index.

Recenzii

“‘This is a capital textbook of functional analysis, measure theory and operator theory, excellently written by an experienced author. The book is based on undergraduate courses of functional analysis taught at the Department of Mathematics of Kharkov University by the author since 1990.’ … the author is to be commended for writing this altogether remarkable and highly recommended book.” (Dirk Werner, zbMATH 1408.46002, 2019)

Notă biografică

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. 

Textul de pe ultima copertă

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.

Caracteristici

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