Isotropic Shearlet Analogs for L 2(ℝ k ) and Localization Operators

In this article we present a new multi-dimensional transformation which contains directional components and which generalizes certain qualities of shearlet transforms. This is achieved by means of exploiting representations of the extended metaplectic group. We study the properties of this new family of isotropic shearlet transformations and of their associated Lie groups, including structural results of the transform spaces. This family yields localization operators which have desirable properties. The Wick symbols for these operators are associated with a well-defined calculus. We also provide simple constructions of families of such reproducing functions. In addition, we analyze an example which shows the uniqueness of this new generalized shearlet transform.

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