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

ISBN-13: 9781611972306 / Angielski / Twarda / 2012 / 260 str.

Yutaka Yamamoto

Opis

A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.

Spis treści

Preface; Glossary of symbols; 1. Vector spaces revisited; 2. Normed linear spaces and Banach spaces; 3. Inner product and Hilbert spaces; 4. Dual spaces; 5. The space L(X,Y) of linear operators; 6. Schwartz distributions; 7. Fourier series and Fourier transform; 8. Laplace transform; 9. Hardy spaces; 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.