Preliminaries.- Semi-norms.- Applications of the Baire-Hausdorff Theorem.- The Orthogonal Projection and F. Riesz' Representation Theorem.- The Hahn-Banach Theorems.- Strong Convergence and Weak Convergence.- Fourier Transform and Differential Equations.- Dual Operators.- Resolvent and Spectrum.- Analytical Theory of Semi-groups.- Compact Operators.- Normed Rings and Spectral Representation.- Other Representation Theorems in Linear Spaces.- Ergodic Theory and Diffusion Theory.- The Integration of the Equation of Evolution.
