Dilational Symmetries of Decomposition and Coorbit Spaces

02.06.2023 09:45 - 11:15

Hartmut Führ (RWTH Aachen University)

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 present a variety of examples, and a general characterization for shearlet dilation groups. Here the coarse geometric criterion leads to a sharp algebraic characterization of coorbit compatible matrices.


K. Gröchenig, L. Liehr, J. L. Romero and I. Shafkulovska