Linear operator theory in engineering and science

Abstract

From the authors' preface: "The goal of this book is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the definition-theorem-proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. "The text can be used by students with various levels of preparation. However, the typical student is probably a first-year graduate student in engineering, one of the formal sciences, or mathematics. It is also possible to use this book as a text for a senior-level course. In order to facilitate students with varying backgrounds, a number of appendices covering useful mathematical topics have been included. Moreover, there has also been an attempt to make the pace in the beginning more gradual than that of later chapters." Table of Contents: Preface; Chapter 1, Introduction; Chapter 2, Set-theoretic structure; Chapter 3, Topological structure, Part A, Introduction to metric spaces, Part B, Some deeper metric space concepts; Chapter 4, Algebraic structure, Part A, Introduction to linear spaces, Part B, Further topics; Chapter 5, Combined topological and algebraic structure, Part A, Banach spaces, Part B, Hilbert spaces, Part C, Special operators; Chapter 6, Analysis of linear operators (compact case), Part A, An illustrative example, Part B, The spectrum, Part C, Spectral analysis; Chapter 7, Analysis of unbounded operators; Appendix A, The H�lder, Schwarz, and Minkowski inequalities; Appendix B, Cardinality; Appendix C, Zorn's lemma; Appendix D, Integration and measure theory; Appendix E, Probability spaces and stochastic processes; Index of symbols; Index.