Stone's Theorem on One-parameter Unitary Groups
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High Quality Content by WIKIPEDIA articles! In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis which establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space H and one-parameter families of unitary operators {U_t}_{t in mathbb{R}} which are strongly continuous, that is lim_{t rightarrow t_0} U_t xi = U_{t_0} xi quad forall t_0 in mathbb{R}, xi in H and are homomorphisms: U_{t+s} = U_t U_s. quad Such one-parameter families are ordinarily referred to as strongly continuous one-parameter unitary groups. The…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis which establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space H and one-parameter families of unitary operators {U_t}_{t in mathbb{R}} which are strongly continuous, that is lim_{t rightarrow t_0} U_t xi = U_{t_0} xi quad forall t_0 in mathbb{R}, xi in H and are homomorphisms: U_{t+s} = U_t U_s. quad Such one-parameter families are ordinarily referred to as strongly continuous one-parameter unitary groups. The theorem is named after Marshall Stone who formulated and proved this theorem in 1932.