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9781611972306 Academic Inspection Copy

From Vector Spaces to Functional Analysis

Introduction to Functional Analysis with Applications
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Provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigour. From Vector Spaces to Function Spaces presents an easily-accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.
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.
Preface Glossary of Symbols Chapter 1: Vector Spaces Revisited Chapter 2: Normed Linear Spaces and Banach Spaces Chapter 3: Inner Product and Hilbert Spaces Chapter 4: Dual Spaces Chapter 5: The Space L(X,Y) of Linear Operators Chapter 6: Schwartz Distributions Chapter 7: Fourier Series and Fourier Transform Chapter 8: Laplace Transform Chapter 9: Hardy Spaces Chapter 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.
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