On the frame set of the second-order B-spline
Document Type
Article
Publication Date
1-1-2023
Abstract
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.
Identifier
85138031390 (Scopus)
Publication Title
Applied and Computational Harmonic Analysis
External Full Text Location
https://doi.org/10.1016/j.acha.2022.08.007
e-ISSN
1096603X
ISSN
10635203
First Page
237
Last Page
250
Volume
62
Grant
DMS 1814253
Fund Ref
National Science Foundation
Recommended Citation
Atindehou, A. Ganiou D.; Frederick, Christina; Kouagou, Yébéni B.; and Okoudjou, Kasso A., "On the frame set of the second-order B-spline" (2023). Faculty Publications. 2149.
https://digitalcommons.njit.edu/fac_pubs/2149