Applications of Functional Analysis and Operator Theory

Vivian Hutson, John S. Pym and Michael J. Cloud (Eds.)9780080527314, 9780444517906, 0444517901

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. Key Features – Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. – Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. – Introduces each new topic with a clear, concise explanation. – Includes numerous examples linking fundamental principles with applications. – Solidifies the reader’s understanding with numerous end-of-chapter problems. · Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. · Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. · Introduces each new topic with a clear, concise explanation. · Includes numerous examples linking fundamental principles with applications. · Solidifies the reader’s understanding with numerous end-of-chapter problems.

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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 ℳp 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