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We define localized modulation maps and modulation spaces of symbols suitedto the study of Rieffel's deformation quantization pseudodifferential calculus.They are used to generate Hilbert space representations for the quantized$C^*$-algebras, starting from covariant representations of the correspondingtwisted $C^*$-dynamical system. In the case of an Abelian undeformed algebra,orthogonal relations and extra information about the representations areobtained.

Modulation Spaces and Representations for Rieffel's Quantization