Stone's Theorem On One-parameter Unitary Groups
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
which are strongly continuous, that is
and are homomorphisms:
Such one-parameter families are ordinarily referred to as strongly continuous one-parameter unitary groups. The theorem was proved by Marshall Stone (1930, 1932). Von Neumann (1932) showed that the condition that Ut is strongly continuous can be relaxed to say that it is weakly measurable, at least when the Hilbert space is separable.
Read more about Stone's Theorem On One-parameter Unitary Groups: Formal Statement, Example, Applications, Generalizations
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