Abstract
We define two-wavelet localization operators in the setting of homogeneous spaces. We prove that they are in the trace class S 1 and give a trace formula for them. Then we show that two-wavelet operators on locally compact and Hausdorff groups endowed with unitary and square-integrable representations, general Daubechies operators and two-wavelet multipliers can be seen as two-wavelet localization operators on appropriate homogeneous spaces. Thus we give a unifying view concerning the three classes of linear operators. We also show that two-wavelet localization operators on $$\mathbb{R}$$ , considered as a homogeneous space, under the action of the affine group U are two-wavelet multipliers
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