Preface About the Author PartⅠ General Theory 1 Topological Vector Spaces Introduction Separation properties Linear mappings Finite-dimensional spaces Metrization Boundedness and continuity Seminorms and local convexity Quotient spaces Examples Exercises 2 Completeness Baire category The Banach-Steinhaus theorem The open mapping theorem The closed graph theorem Bilinear mappings Exercises 3 Convexity The Hahn-Banach theorems Weak topologies Compact convex sets Vector-valued integration Holomorphic functions Exercises 4 Dualityin Banach Spaces The normed dual of a normed space Adjoints Compact operators Exercises 5 Some Applications A continuity theorem Closed subspaces of LP-spaces The range of a vector-valued measure A generalized Stone-Weierstrass theorem Two interpolation theorems Kakutani's fixed point theorem Haar measure on compact groups Uncomplemented subspaces Sums of Poisson kernels Two more fixed point theorems Exercises PartⅡ Distributions and Fourier Transforms 6 Test Functions and Distributions Introduction Test function spaces Calculus with distributions Localization Supports of distributions Distributions as derivatives Convolutions Exercises 7 Fourier Transforms Basic properties Tempered distributions Paley-Wiener theorems Sobolev's lemma Exercises 8 Applications to Differential Equations Fundamental solutions Elliptic equations Exercises …… Part Ⅲ Banach Algebras and Spectral Theory Appendix A Compactness and Continuity Appendix B Notes and Comments Bibliography List of Special Symbols Index
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