Essential Operators: Spectrum and Resolvent Set

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Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

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Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores the matrix representation of operators and basis transformation in linear algebra.

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