
From Vector Spaces to Functional Analysis
Introduction to Functional Analysis with Applications
Yutaka Yamamoto(Author)
Society for Industrial & Applied Mathematics,U.S. (Publisher)
Published on 30. August 2012
Book
Hardback
282 pages
978-1-61197-230-6 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Dimensions
Height: 247 mm
Width: 174 mm
Thickness: 22 mm
Weight
770 gr
ISBN-13
978-1-61197-230-6 (9781611972306)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
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.
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.