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.
A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for 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.