Functional Analysis

  1. Spectral Theory
    1. Basic Spectral Concepts
      1. Eigenvalues and Eigenvectors
        1. Spectrum of an Operator
          1. Point Spectrum
            1. Continuous Spectrum
              1. Residual Spectrum
              2. Resolvent Set
                1. Resolvent Operator
                2. Spectral Properties
                  1. Spectral Radius
                    1. Spectral Radius Formula
                      1. Properties of Spectrum
                        1. Spectral Mapping Theorem
                        2. Compact Operators
                          1. Definition and Examples
                            1. Properties of Compact Operators
                              1. Space of Compact Operators
                                1. Spectral Theory of Compact Operators
                                  1. Riesz-Schauder Theory
                                    1. Spectral Decomposition
                                    2. Fredholm Alternative
                                    3. Self-Adjoint Operators
                                      1. Adjoint Operators
                                        1. Self-Adjoint Operators
                                          1. Properties of Self-Adjoint Operators
                                            1. Spectral Theorem for Compact Self-Adjoint Operators
                                              1. Spectral Theorem for Bounded Self-Adjoint Operators
                                                1. Functional Calculus

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                                              9. Advanced Topics