TITLE:
On the Frame Set for the 3-Spline
AUTHORS:
Abdou Ganiou Débayo Atindehou
KEYWORDS:
Gabor Frames, Frame Set, 3-Splines, Compactly Dual Frame
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.5,
May
20,
2022
ABSTRACT: This paper investigates the fine structure of the Gabor frame generated by the B-spline B3. In other words, one extends the known part of the Gabor frame set for the 3-spline with the construction of the compactly supported dual windows. The frame set of the function B3 is the subset of all parameters (a,b) ∈ R2+ for which the time-frequency shifts of B3 along aZ × bZ form a Gabor frame for L2(R).