Functional Analysis

Front Matter....Pages I-XII Preliminaries....Pages 1-22 Semi-norms....Pages 23-68 Applications of the Baire-Hausdorff Theorem....Pages 68-81 The Orthogonal Projection and F. Riesz’ Representation Theorem....Pages 81-101 The Hahn-Banach Theorems....Pages 102-119 Strong Convergence and Weak Convergence....Pages 119-145 Fourier Transform and Differential Equations....Pages 145-193 Dual Operators....Pages 193-208 Resolvent and Spectrum....Pages 209-231 Analytical Theory of Semi-groups....Pages 231-274 Compact Operators....Pages 274-293 Normed Rings and Spectral Representation....Pages 294-362 Other Representation Theorems in Linear Spaces....Pages 362-378 Ergodic Theory and Diffusion Theory....Pages 379-411 The Integration of the Equation of Evolution....Pages 411-438 Back Matter....Pages 439-468