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In this paper we introduce a transformation of Fourier-Stieltjes type acting on C *-algebra valued measures on a locally compact group. This transformation is related to an action of the group on a Hilbert C *module. We obtain among other results an integral representation of a set of bounded operators and the analogue of the convolution theorem.

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This paper deals with the Fourier-Stieltjes transform of C∗-algebra valued measures. We construct an involution on the space of such measures, define their Fourier-Stieltjes transform and derive a convolution theorem.