Lecture Notes on Functional Analysis

With Applications to Linear Partial Differential Equations

Alberto Bressan

• Publisher: American Mathematical Society
• Year: 2012
• ISBN:
  9780821894064
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations.The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.

Table of contents

• Cover
• Title page
• Contents
• Preface
• Chapter 1. Introduction
• Chapter 2. Banach spaces
• Chapter 3. Spaces of continuous functions
• Chapter 4. Bounded linear operators
• Chapter 5. Hilbert spaces
• Chapter 6. Compact operators on a Hilbert space
• Chapter 7. Semigroups of linear operators
• Chapter 8. Sobolev spaces
• Chapter 9. Linear partial differential equations
• Chapter 10. Background material
• Summary of notation
• Bibliography
• Index
• Back Cover