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

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by Yutaka Yamamoto


2012 / xiv + 268 pages / Hardcover / ISBN: 978-1-611972-30-6 / List Price $92.00 / SIAM Member Price $64.40 / Order Code OT127


"The material in this book is tightly put together and the writing style is mathematically sophisticated and precise. The modern style of exposition combined with the appendices result in a book that is self-contained and an excellent reference and learning source for researchers and students with a variety of backgrounds. The choice of topics covered and the clear presentation make the book eminently suited as a senior or graduate level text for a course in general and applied mathematics aimed at students interested in the mathematical foundations of control and signal processing."
- Jan C. Willems, Department of Electrical Engineering, University of Leuven, Belgium

This book 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 rigor. 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.

This book is appropriate for advanced undergraduate or graduate students in science, engineering, or mathematics. It will also be useful to working scientists and engineers who use analytical methods in applied mathematics, systems and control theorists, and practitioners who need basics in mathematics.

About the Author
Yutaka Yamamoto is a professor in the Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto, Japan. His main interest is in system and control theory, particularly the theory of sampled data control systems, its application to digital signal processing, realization and robust control of distributed parameter systems, and related mathematical problems. 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.

ISBN: 9781611972306

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