On a discrete transform of homogeneous decomposition spaces

2020/06/15 by Zeineb Al-Jawahri, Morten Nielsen, Al-Jawahri, Zeineb +1
Mathematics · #41A17 #42B35 #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:41A17 #msc:42B35 #msc:42C15

paper · pdf · doi:10.48550/arxiv.2006.08182

30 pages

arxiv created 2020/06/15 · arxiv updated 2020/06/16

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.

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