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Functional Analysis [1978]

1
Preliminaries
1
Preliminaries on Set Theory and Topology
23
Semi-norms
68
Applications of the Baire-Hausdorff Theorem
79
Measure
81
The Orthogonal Projection and F. Riesz’ Representation Theorem
102
The Hahn-Banach Theorems
119
Integration
119
Strong Convergence and Weak Convergence
145
Fourier Transform and Differential Equations
171
Differentiation
193
Dual Operators
209
Resolvent and Spectrum
227
Banach Spaces
231
Analytical Theory of Semi-groups
274
Compact Operators
294
Normed Rings and Spectral Representation
319
Hilbert Spaces
362
Other Representation Theorems in Linear Spaces
379
Ergodic Theory and Diffusion Theory
389
Measure and Topology
418
The Integration of the Equation of Evolution
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