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

The frame set of a function g is an element of L2(R) is the set of all parameters (a, b) is an element of R2+ for which the collection of time-frequency shifts of g along aZ x 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. (c) 2022 Elsevier Inc. All rights reserved.