We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a certain metric in frequency domain. We formulate versions of this phenomenon both for the decomposition and coorbit space settings.

We then apply the general results to a particular class of dilation groups, the so-called shearlet dilation groups. We present a general, algebraic characterization of matrices that are coorbit compatible with a given shearlet dilation group. We explicitly determine the groups of compatible dilations, for a variety of concrete examples.

我们研究了矩阵膨胀下一般小波coorbit空间和Besov型分解空间的不变性。我们证明这些矩阵可以用相对于频域中某个度量的准等距性质来表征。我们针对分解和坐标空间设置制定了这种现象的版本。

然后，我们将一般结果应用于特定类别的扩张群，即所谓的剪切波扩张群。我们提出了与给定剪切波扩张群协同兼容的矩阵的一般代数表征。对于各种具体示例，我们明确确定了兼容扩张的组。