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essential self-adjointness the spectral theory of Hermitian operators self-adjoint hermitian operators resolution of the identity spectral theorem for self-adjoint operators pure point spectrum spectral multiplicity theory unitarily equivalent unitarily non-equivalent self-adjoint operators self-adjoint operator self-adjoint linear operator implies Self-adjoint operator#Spectral multiplicity theory Hermitian unitary equivalence self-adjointness Self-adjoint_operator#Symmetric operators Self-adjoint_operator Self-adjoint unbounded operators Self-adjoint operator#Self-adjoint extensions in quantum mechanics spectral theorem symmetric operators Self-adjoint operator#Extensions of symmetric operators symmetric operator Spectral theorem Hermitian operator Hermitian operators