Applications of Functional Analysis and Operator Theory

✍ Scribed by Vivian Hutson, John S. Pym and Michael J. Cloud (Eds.)

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Leaves: 443
• Series: Mathematics in Science and Engineering 200
• Edition: 2
• Category: Library

✦ Synopsis

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

✦ Table of Contents

Content:
Preface
Pages v-vii
V. Hutson, J.S. Pym, M.J. Cloud

Acknowledgements
Page ix

Chapter 1 Banach spaces Original Research Article
Pages 1-38

Chapter 2 Lebesgue integration and the ℳ_p spaces Original Research Article
Pages 39-64

Chapter 3 Foundations of linear operator theory Original Research Article
Pages 65-113

Chapter 4 Introduction to nonlinear operators Original Research Article
Pages 115-146

Chapter 5 Compact sets in Banach spaces Original Research Article
Pages 147-156

Chapter 6 The adjoint operator Original Research Article
Pages 157-187

Chapter 7 Linear compact operators Original Research Article
Pages 189-215

Chapter 8 Nonlinear compact operators and monotonicity Original Research Article
Pages 217-239

Chapter 9 The spectral theorem Original Research Article
Pages 241-268

Chapter 10 Generalized eigenfunction expansions associated with ordinary differential equations Original Research Article
Pages 269-301

Chapter 11 Linear elliptic partial differential equations Original Research Article
Pages 303-342

Chapter 12 The finite element method Original Research Article
Pages 343-357

Chapter 13 Introduction to degree theory Original Research Article
Pages 359-383

Chapter 14 Bifurcation theory Original Research Article
Pages 385-407

References Original Research Article
Pages 409-416

List of symbols
Pages 417-420

Index
Pages 421-426