On a Fourier Expansion in Continuous Crossed Products

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Let (M, R, α) be a separable continuous W*-dynamical system such that M is R-finite. <BR>Then any element in the crossed product RαM of M by α can be expressed as a vector valued tempered distribution DqTη which is a weak* limit of Tξ, ξ∈K(R;\mathfrak{B}) in the dual space SU(R;\mathfrak{y})* of a generalized Schwartz space SU(R;\mathfrak{y}), where K(R;\mathfrak{B}) is the Tomita algebra corresponding to RαM.

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