Two-Wavelet Localization Operators on Homogeneous Spaces and Their Traces

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