On the Frame Set for the 3-Spline

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 ) ∈L2(R) for which the time-frequency shifts of B3 along aZ× bZ form a Gabor frame for L2 (R) .