Frame sets for a class of compactly supported continuous functions

Abstract

The frame set of a function g ∈ L 2 (R) is the subset of all parameters (a, b) ∈ R 2+ for which the time-frequency shifts of g along aZ × bZ form a Gabor frame for L 2 (R). In this paper, we investigate the frame set of a class of compactly supported continuous functions which includes the B-splines. In particular, we add some new points to the frame sets of these functions. In the process, we generalize and unify some recent results on the frame sets for this class of functions.