Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations (Graduate Studies in 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. Readership: Graduate students interested in functional analysis and partial differential equations. 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 Alberto Bressan. Includes Bibliographical References (pages 245-246) And Index.