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

Yamamoto, Yutaka

Society for Industrial & Applied Mathematics,U.S.（2012/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 282 p.
• 言語 ENG
• 商品コード 9781611972306
• DDC分類 515.7

Full 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.

Contents

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.