From Vector Spaces to Functional Analysis

Introduction to Functional Analysis with Applications

Inbunden, Engelska, 2012

1 239 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2012-08-30
Mått:182 x 259 x 22 mm
Vikt:766 g
Format:Inbunden
Språk:Engelska
Antal sidor:282
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9781611972306

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Mer om författaren

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.

Innehållsförteckning

PrefaceGlossary of SymbolsChapter 1: Vector Spaces RevisitedChapter 2: Normed Linear Spaces and Banach SpacesChapter 3: Inner Product and Hilbert SpacesChapter 4: Dual SpacesChapter 5: The Space L(X,Y) of Linear OperatorsChapter 6: Schwartz DistributionsChapter 7: Fourier Series and Fourier TransformChapter 8: Laplace TransformChapter 9: Hardy SpacesChapter 10: Applications to Systems and ControlAppendix A: Some Background in Sets, Mappings, TopologyAppendix B: Table of Laplace TransformsSolutionsBibliographical NotesBibliographyIndex.