From Vector Spaces to Function Spaces: Introduction to Functional Analysis with Applications
Society for Industrial and Applied Mathematics, 10/4/2012
EAN 9781611972306, ISBN10: 1611972302
Hardcover, 260 pages, 24.7 x 17.4 x 2.2 cm
Language: English
Analytical methods of applied mathematics are the subject of this book, which takes the reader from elementary notions of functional analysis to an advanced discussion of systems and control theory. The text begins by reviewing the basics of vector spaces, the theory of which is developed further to include Banach and Hilbert spaces. This provides a strong foundation in functional analysis from which the author can launch a penetrating discussion of duality, distributions, Fourier and Laplace transforms and Hardy spaces. Finally, cutting-edge applications of these techniques to systems and control theory are presented. This text is designed to be useful to working scientists, engineers and students and will appeal to those unfamiliar with the material covered. The author's modern style of exposition provides the motivations of definitions and the ideas underlying proofs without sacrificing mathematical rigour.
Preface
Glossary of symbols
1. Vector spaces revisited
2. Normed linear spaces and Banach spaces
3. Inner product and Hilbert spaces
4. Dual spaces
5. The space L(X,Y) of linear operators
6. Schwartz distributions
7. Fourier series and Fourier transform
8. Laplace transform
9. Hardy spaces
10. Applications to systems and control
Appendix A. Some background in sets, mappings, topology
Appendix B. Table of Laplace transforms
Solutions
Bibliographical notes
Bibliography
Index.