Dilational Symmetries of Decomposition and Coorbit Spaces
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.
Cite
@article{arxiv.2303.17938,
title = {Dilational Symmetries of Decomposition and Coorbit Spaces},
author = {Hartmut Führ and Reihaneh Raisi Tousi},
journal= {arXiv preprint arXiv:2303.17938},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2105.13730