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arXiv · 2303.17938

Dilational Symmetries of Decomposition and Coorbit Spaces

Hartmut Führ·Reihaneh Raisi Tousi
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Abstract

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 the are coorbit compatible with a given shearlet dilation group. We determine the groups of compatible dilations for a variety of concrete examples.

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Hartmut Führ, Reihaneh Raisi Tousi. 2023-03-31. Dilational Symmetries of Decomposition and Coorbit Spaces. https://arxiv.org/abs/2303.17938

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