From Vector Spaces to Function Spaces Introduction to Functional Analysis with Applications

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.

This book provides a treatment of analytic methods of applied mathematics. The text begins with a review of vector spaces and goes on to explore functional analysis, concluding with applications to control and systems theory. This book will appeal to working scientists, engineers and students.

Yutaka Yamamoto is a professor at the department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Japan. He is a recipient of the G. S. Axelby Outstanding Paper Award of the IEEE Control Systems Society, the Commendation for Science and Technology by the Minister of Education in Japan, the Distinguished Member Award of the Control Systems Society of the IEEE and various other awards. He has authored or co-authored more than 200 journal or conference papers. He is currently President-elect of the IEEE Control Systems Society and past President of ISCIE Japan. He is a fellow of the IEEE and ISCIE, Japan.