| Contents 0. Preliminaries 1. Set Theory 2. Topological Spaces 3. Measure Spaces 4. Linear Spaces I. Semi-nonns 1. Semi-nonns and Locally Convex Linear Topological Spaces 2. Nonns and Quasi-nonns 3. Examples of Normed Linear Spaces 4. Examples of Quasi-nonned Linear Spaces 5. Pre-Hilbert Spaces 6. Continuity of Linear Operators 7. Bounded Sets and Bomologic Spaces 8. Generalized Functions and Generalized Derivatives 9. B-spaces and F-spaces 10. Tbe Completion 11. Factor Spaces of a B-space 12. The Partition of Unity 13. Generalized Functions with Compact Support 14. The Direct Product of Generalized Functions II. Applications of the Baire-Hausdorff Theorem 1. The Unifonn Boundedness Theorem and the Resonance Theorem 2. The Vitali-Hahn-Saks Theorem 3. The Termwise Differentiability of a Sequence of Generalized Functions 4. The Principle ot the Condensation of Singularities 5. The Open Mapping Theorem 6. The Closed Graph Theorem 7. An Application of the Closed Graph Theorem (Hormander's Theorem) III. The Orthogonal Projection and F. Riesz Representation Theo-rem 1. The Orthogonal Projection 2. "Nearly Orthogonal" Elements …… IV. The Hahn-Banach Theorems V. Strong Convergence and Weak Convergence VI. Fourier Transform and Differential Equations VII. Dual Operators VIII. Resolvent and Spectrum IX. Analytical Theory of Semi-groups X Compact Operators XI. Nonned Rings and Spectral Representation XII. Other Representation Theorems in Linear Spaces XIIT. Ergodic Theory and Diffusion Theory XIV The Integration of the Equation of Evolution Supplementary Notes Bibliography Index Notation of Spaces |
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