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Course Outline
- A quick review of basic functional analysis.
- Compact linear operator on normed spaces.
- Properties of compact linear operators.
- Spectral of compact linear operators.
- Operator equations involving compact linear operators.
- Spectral properties of bounded self adjoint operators.
- Positive operators.
- Square root of positive operators.
- Projection operators.
- Spectral family.
- Spectral family of a bounded self adjoint operators.
- Unbounded linear operators in Hilbert spaces.
- Hilbert adjoint operators.
- Symmetric and self adjoint operators.
- Multiplication and differentiation operators.
- Application of unbounded operators.