Isotropic Shearlet Analogs for L 2(ℝ k ) and Localization Operators
Isotropic Shearlet Analogs for L 2(ℝ k ) and Localization Operators
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DOI：
10.1080/01630563.2012.682137
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发表时间：
2012-07
影响因子：
1.2
通讯作者：
W. Czaja;E. King
中科院分区：
文献类型：
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作者：
W. Czaja;E. King
在这篇文章中，我们提出了一个新的多维变换，其中包含方向分量，并推广了某些性质的剪切波变换。这是通过利用扩展的元群的表示来实现的。我们研究这个新的家庭的各向同性剪切波变换及其相关的李群的性质，包括结构的结果的变换空间。这个家庭产生的本地化运营商具有理想的性能。这些运算符的威克符号与定义良好的微积分相关联。我们还提供了简单的家庭建设这样的再生功能。此外，我们分析了一个例子，这表明这种新的广义剪切波变换的唯一性。
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.