Foreword; Introduction; 1. Inner product spaces; 2. Normed spaces; 3. Hilbert and Banach spaces; 4. Orthogonal expansions; 5. Classical Fourier series; 6. Dual spaces; 7. Linear operators; 8. Compact operators; 9. Sturm-Liouville systems; 10. Green's functions; 11. Eigenfunction expansions; 12. Positive operators and contractions; 13. Hardy spaces; 14. Interlude: complex analysis and operators in engineering; 15. Approximation by analytic functions; 16. Approximation by meromorphic functions; Appendix; References; Answers to selected problems; Afterword; Index of notation; Subject index.

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This textbook is an introduction to the theory of Hilbert space and its applications.

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' ... the author's style is a delight. Each topic is carefully motivated and succinctly presented, and the exposition is enthusiastic and limpid ... Young has done a really fine job in presenting a subject of great mathematical elegance as well as genuine utility, and I recommend it heartily.' Times Higher Education Supplement

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