On a discrete transform of homogeneous decomposition spaces
Functional Analysis
2020-06-16 v1
Abstract
We introduce almost diagonal matrices in the setting of (anisotropic) discrete homogeneous Triebel-Lizorkin type spaces and homogeneous modulation spaces, and it is shown that the class of almost diagonal matrices is closed under matrix multiplication. We then connect the results to the continuous setting and show that the "change of frame" matrix for a pair of time-frequency frames, with suitable decay properties, is almost diagonal. As an application of this result, we consider a construction of compactly supported frame expansions for homogeneous decomposition spaces of Triebel-Lizorkin type and for the associated modulation spaces.
Cite
@article{arxiv.2006.08182,
title = {On a discrete transform of homogeneous decomposition spaces},
author = {Zeineb Al-Jawahri and Morten Nielsen},
journal= {arXiv preprint arXiv:2006.08182},
year = {2020}
}
Comments
30 pages