Functional Analysis

Indeholder "Preface", "Part I. General Theory", "Chapter 1 Topological Vector Spaces", " Introduction", " Separation properties", " Linear mappings", " Finite-dimensional spaces", " Metrization", " Boundedness and continuity", " Seminorms and local convexity", " Quotient spaces", " Examples", "

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Exercises", "Chapter 2 Completeness", " Baire category", " The Banach-Steinhaus theorem", " The open mapping theorem", " The closed graph theorem", " Bilinear mappings", " Exercises", "Chapter 3. Convexity", " The Hahn-Banach theorems", " Weak topologies", " Compact convex sets", " Vector-valued integration", " Holomorphic functions", " Exercises", "Chapter 4. Duality in Banach Spaces", " The normed dual of a normed space", " Adjoints", " Compact operators", " Exercises", "Chapter 5. Some Applications", " A continuity theorem", " Closed subspaces of LF-spaces", " The range of a vector-valued measure", " A generalized Stone-Weierstrass theorem", " Two interpolation theorems", " A fixed point theorem", " Haar measure on compact groups", " Uncomplemented subspaces", " Exercises", "Part II. Distributions and Fourier Transforms", "Chapter 6. Test Functions and Distributions", " Introduction", " Test function spaces", " Calculus with distributions", " Localization", " Supports of distributions", " Distributions as derivatives", " Convolutions", " Exercises", "Chapter 7. Fourier Transforms", " Basic properties", " Tempered distributions", " Paley-Wiener theorems", " Sobolev's lemma", " Exercises", "Chapter 8. Applications to Differential Equations", " Fundamental solutions", " Elliptic equations", " Exercises", "Chapter 9. Tauberian Theory", " Wiener's theorem", " The prime number theorem", " The renewal equation", " Exercises", "Part III. Banach Algebras and Spectral Theory", "Chapter 10. Banach Algebras", " Introduction", " Complex homomorphisms", " Basic properties of spectra", " Symbolic calculus", " The group of invertible elements", " Lomonosov's invariant subspace theorem", " Exercises", "Chapter 11. Commutative Banach Algebras", " Ideals and homomorphisms", " Gelfand transforms", " Involutions", " Applications to noncommutative algebras", " Positive functionals", " Exercises", "Chapter 12. Bounded Operators on a Hilbert Space", " Basic facts", " Bounded operators", " A commutativity theorem", " Resolutions of the identity", " The spectral theorem", " Eigenvalues of normal operators", " Positive operators and square roots", " The group of invertible operators", " A characterization of B*-algebras", " Exercises", "Chapter 13. Unbounded Operators", " Introduction", " Graphs and symmetric operators", " The Cayley transform", " Resolutions of the identity", " The spectral theorem", " Semigroups of operators", " Exercises", "Appendix A. Compactness and Continuity", "Appendix B. Notes and Comments", "Bibliography", "List of Special Symbols", "Index".

Denne bog går hen over mit hoved på trods af et bifag i matematik. Lidt flere eksempler ville være rare.

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