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Functional Analysis

Fundamentals and Applications

  • Michel Willem

Part of the Cornerstones book series (COR)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Michel Willem
    Pages 1-20
  3. Michel Willem
    Pages 21-49
  4. Michel Willem
    Pages 51-71
  5. Michel Willem
    Pages 73-92
  6. Michel Willem
    Pages 93-109
  7. Michel Willem
    Pages 111-137
  8. Michel Willem
    Pages 139-156
  9. Michel Willem
    Pages 157-184
  10. Michel Willem
    Pages 185-191
  11. Back Matter
    Pages 205-213

About this book

Introduction

The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional  analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics.

Keywords

Banach spaces Hilbert spaces Lebesque spaces Sobolev spaces distribution theory functional analysis

Authors and affiliations

  • Michel Willem
    • 1
  1. 1.Department of MathematicsUniversité catholique de LouvainLouvain-la-NeuveBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7004-5
  • Copyright Information Springer Science+Business Media, LLC 2013
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7003-8
  • Online ISBN 978-1-4614-7004-5
  • Series Print ISSN 2197-182X
  • Series Online ISSN 2197-1838
  • Buy this book on publisher's site