Functional Analysis

This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem. This text is part of the Walter Rudin Student Series in Advanced Mathematics. Read more... pt. I. General theory. 1. Topological vector spaces -- 2. Completeness -- 3. Convexity -- 4. Duality in Banach spaces -- 5. Some applications -- pt. II. Distributions and Fourier transforms. 6. Test functions and distributions -- 7. Fourier transforms -- 8. Applications to differential equations -- 9. Tauberian theory -- pt. III. Banach algebras and spectral theory. 10. Banach algebras -- 11. Commutative Banach algebras -- 12. Bounded operators on a Hilbert space -- 13. Unbounded operators This Classic Text Is Written For Graduate Courses In Functional Analysis. This Text Is Used In Modern Investigations In Analysis And Applied Mathematics. This New Edition Includes Up-to-date Presentations Of Topics As Well As More Examples And Exercises. New Topics Include Kakutani's Fixed Point Theorem, Lamonosov's Invariant Subspace Theorem, And An Ergodic Theorem. This Text Is Part Of The Walter Rudin Student Series In Advanced Mathematics. Pt. I. General Theory. 1. Topological Vector Spaces -- 2. Completeness -- 3. Convexity -- 4. Duality In Banach Spaces -- 5. Some Applications -- Pt. Ii. Distributions And Fourier Transforms. 6. Test Functions And Distributions -- 7. Fourier Transforms -- 8. Applications To Differential Equations -- 9. Tauberian Theory -- Pt. Iii. Banach Algebras And Spectral Theory. 10. Banach Algebras -- 11. Commutative Banach Algebras -- 12. Bounded Operators On A Hilbert Space -- 13. Unbounded Operators. Walter Rudin. Includes Bibliographical References (p. 412-413) And Index. Part of the Student Series in Advanced Mathematics, this text is written for graduate courses in functional analysis. Used in modern investigations in analysis and applied mathematics, it includes Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem. Written for undergraduate courses, this new edition includes coverage of current topics of research and contains more exercises and examples. New topics covered include: Kakutani's fixed point theorem; Lomonosov's invariant subspace theorem; and an ergodic theorem.