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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
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Stone–von Neumann theorem?
The Stone–von Neumann theorem says that given two unitary groups on a Hilbert space $H$ satisfying the canonical commutation relations (CCR)
$$
U(t)V(s) = e^{-i st} V(s) U(t) \qquad \forall s, t
$$
th …