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

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Yutaka YamamotoSociety for Industrial and Applied Mathematics, 10/4/2012EAN 9781611972306, ISBN10: 1611972302Hardcover, 260 pages, 24.7 x 17.4 x 2.2 cmLanguage: EnglishAnalytical m ethods of applied mathematics are the subject of this book, which takes the reader from elementary notions of functional analysis to an advanced discussion of systems and control theory. The text begins by reviewing the basics of vector spaces, the theory of which is developed further to include Banach and Hilbert spaces. This provides a strong foundation in functional analysis from which the author can launch a penetrating discussion of duality, distributions, Fourier and Laplace transforms and Hardy spaces. Finally, cutting-edge applications of these techniques to systems and control theory are presented. This text is designed to be useful to working scientists, engineers and students and will appeal to those unfamiliar with the material covered. The author's modern style of exposition provides the motivations of definitions and the ideas underlying proofs without sacrificing mathematical rigour.PrefaceGlossary of symbols1. Vector spaces revisited2. Normed linear spaces and Banach spaces3. Inner product and Hilbert spaces4. Dual spaces5. The space L(X,Y) of linear operators6. Schwartz distributions7. Fourier series and Fourier transform8. Laplace transform9. Hardy spaces10. Applications to systems and controlAppendix A. Some background in sets, mappings, topologyAppendix B. Table of Laplace transformsSolutionsBibliographical notesBibliographyIndex. Show more