Table of Contents:
  • 0. Preliminaries
  • I. Semi-norms
  • II. Applications of the Baire-Hausdorff Theorem
  • III. The Orthogonal Projection and F. Riesz' Representation Theorem
  • 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. Normed Rings and Spectral Representation
  • XII. Other Representation Theorems in Linear Spaces
  • XIII. Ergodic Theory and Diffusion Theory
  • XIV. The Integration of the Equation of Evolution