Linear Functional Analysis: An Application-Oriented Introduction

✍ Scribed by Hans Wilhelm Alt (auth.)

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 446
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XII
Introduction....Pages 1-8
Preliminaries....Pages 9-36
Function spaces....Pages 37-94
Subsets of function spaces....Pages 95-140
Linear operators....Pages 141-162
Linear functionals....Pages 163-218
Uniform boundedness principle....Pages 219-226
Weak convergence....Pages 227-283
Finite-dimensional approximation....Pages 285-318
Compact operators....Pages 319-372
Spectrum of compact operators....Pages 373-387
Self-adjoint operators....Pages 389-418
Back Matter....Pages 419-435

✦ Subjects

Functional Analysis; Partial Differential Equations