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A Course in Functional Analysis and Measure Theory

  • Vladimir Kadets

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Vladimir Kadets
    Pages 1-32
  3. Vladimir Kadets
    Pages 33-77
  4. Vladimir Kadets
    Pages 79-96
  5. Vladimir Kadets
    Pages 97-136
  6. Vladimir Kadets
    Pages 159-180
  7. Vladimir Kadets
    Pages 203-230
  8. Vladimir Kadets
    Pages 231-248
  9. Vladimir Kadets
    Pages 249-275
  10. Vladimir Kadets
    Pages 311-341
  11. Vladimir Kadets
    Pages 343-370
  12. Vladimir Kadets
    Pages 371-407
  13. Vladimir Kadets
    Pages 409-430
  14. Vladimir Kadets
    Pages 431-468
  15. Vladimir Kadets
    Pages 469-500
  16. Vladimir Kadets
    Pages 501-523
  17. Back Matter
    Pages 525-539

About this book

Introduction

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

Authors and affiliations

  • Vladimir Kadets
    • 1
  1. 1.School of Mathematics and Computer ScienceV. N. Karazin Kharkiv National UniversityKharkivUkraine

Bibliographic information

  • 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
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