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Linear Functional Analysis

An Application-Oriented Introduction

  • Textbook
  • © 2016

Overview

Authors:
  1. Hans Wilhelm Alt

    1. Department of Mathematics, Technische Universität München , Garching near Munich, Germany

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  • A complete, self-contained introduction to linear functional analysis
  • Includes topics such as operator theory, distributions, Sobolev spaces
  • Features many solved exercises

Part of the book series: Universitext (UTX)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    • Hans Wilhelm Alt
    Pages 1-8

  3. Preliminaries

    • Hans Wilhelm Alt
    Pages 9-36

  4. Function spaces

    • Hans Wilhelm Alt
    Pages 37-94

  5. Subsets of function spaces

    • Hans Wilhelm Alt
    Pages 95-140

  6. Linear operators

    • Hans Wilhelm Alt
    Pages 141-162

  7. Linear functionals

    • Hans Wilhelm Alt
    Pages 163-218

  8. Uniform boundedness principle

    • Hans Wilhelm Alt
    Pages 219-226

  9. Weak convergence

    • Hans Wilhelm Alt
    Pages 227-283

  10. Finite-dimensional approximation

    • Hans Wilhelm Alt
    Pages 285-318

  11. Compact operators

    • Hans Wilhelm Alt
    Pages 319-372

  12. Spectrum of compact operators

    • Hans Wilhelm Alt
    Pages 373-387

  13. Self-adjoint operators

    • Hans Wilhelm Alt
    Pages 389-418

  14. Back Matter

    Pages 419-435
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Keywords

About this book

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions. Moreover, there are a number of appendices, for example on Lebesgue integration theory.

A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

Reviews

“The volume under review deals rigorously with mathematical models of certain applicability to real world problems. From this viewpoint it is a significant contribution to a currently active area of research. … this book will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations. … I wholeheartedly recommend this book both as a textbook, as well as for independent study.” (Vicenţiu D. Rădulescu, zbMATH 1358.46002, 2017)

Authors and Affiliations

  • Department of Mathematics, Technische Universität München , Garching near Munich, Germany

    Hans Wilhelm Alt

About the author

Professor Alt's work has had a significant impact on the areas of applied analysis and partial differential equations, in particular in the applications to mechanics and thermodynamics. Recently, he worked in the mathematical theory of phase transition and made contributions to the entropy principle. Alt was professor at the Institute of Applied Mathematics at the University of Bonn, and since 2011 lectures as Honorary Professor at the Technical University of Munich.

Bibliographic Information

  • Book Title: Linear Functional Analysis

  • Book Subtitle: An Application-Oriented Introduction

  • Authors: Hans Wilhelm Alt

  • Translated by: Robert Nürnberg

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4471-7280-2

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London 2016

  • Softcover ISBN: 978-1-4471-7279-6Published: 14 July 2016

  • eBook ISBN: 978-1-4471-7280-2Published: 06 July 2016

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 435

  • Number of Illustrations: 19 b/w illustrations

  • Additional Information: Original German edition with the title Lineare Funktionalanalysis (6th ed.) published by Springer-Verlag Berlin Heidelberg, 2012

  • Topics: Functional Analysis, Partial Differential Equations

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