@article{29ed8c5e3ed442c5a2b540e7573d4945,
title = "On the frame set of the second-order B-spline",
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.",
keywords = "B-splines, Frame set, Gabor frames",
author = "Atindehou, {A. Ganiou D.} and Christina Frederick and Kouagou, {Y{\'e}b{\'e}ni B.} and Okoudjou, {Kasso A.}",
note = "Funding Information: Part of this work was completed while the first-named author was a visiting graduate student in the Department of Mathematics at the University of Maryland during the Fall 2017 semester. He would like to thank the Department for its hospitality and the African Center of Excellence in Mathematics and Application (CEA-SMA) at the Institut de Math{\'e}matiques et de Sciences Physiques (IMSP) for funding his visit. K.A. Okoudjou was partially supported by a grant from the Simons Foundation # 319197 , by ARO grant W911NF1610008 , and the National Science Foundation grant DMS 1814253 . Funding Information: Part of this work was completed while the first-named author was a visiting graduate student in the Department of Mathematics at the University of Maryland during the Fall 2017 semester. He would like to thank the Department for its hospitality and the African Center of Excellence in Mathematics and Application (CEA-SMA) at the Institut de Math{\'e}matiques et de Sciences Physiques (IMSP) for funding his visit. K.A. Okoudjou was partially supported by a grant from the Simons Foundation # 319197, by ARO grant W911NF1610008, and the National Science Foundation grant DMS 1814253. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2023",
month = jan,
doi = "10.1016/j.acha.2022.08.007",
language = "English (US)",
volume = "62",
pages = "237--250",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Academic Press Inc.",
}