On a discrete transform of homogeneous decomposition spaces

Zeineb Al-Jawahri, Morten Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)


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.
Original languageEnglish
JournalApplied and Computational Harmonic Analysis
Pages (from-to)41-70
Number of pages30
Publication statusPublished - 2021


  • Anisotropic smoothness space
  • Besov space
  • Decomposition space
  • Homogeneous space
  • Modulation space
  • α-Modulation space


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