On the frame set of the second-order B-spline

A. Ganiou D. Atindehou, Christina Frederick, Yébéni B. Kouagou, Kasso A. Okoudjou

Research output: Contribution to journalArticlepeer-review


The frame set of a function g∈L2(R) is the set of all parameters (a,b)∈R+2 for which the collection of time-frequency shifts of g along aZ×bZ form a Gabor frame for L2(R). Finding the frame set of a given function remains a challenging open problem in time-frequency analysis. In this paper, we establish new regions of the frame set of the second-order B-spline. Our method uses the compact support of this function to partition a subset of the putative frame set and finds an explicit dual window function in each subregion. Numerical evidence indicates the existence of further regions belonging to the frame set.

Original languageEnglish (US)
Pages (from-to)237-250
Number of pages14
JournalApplied and Computational Harmonic Analysis
StatePublished - Jan 2023

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • B-splines
  • Frame set
  • Gabor frames


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