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

被引：1
|
作者：
Atindehou, A. Ganiou D. [1 ]
Frederick, Christina [2 ]
Kouagou, Yebeni B.
Okoudjou, Kasso A. [3 ]
机构：
[1] Univ Abomey Calavi, Dept Math, 01 BP 4521, Cotonou, Benin
[2] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA
[3] Tufts Univ, Dept Math, Medford, MA 02155 USA
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2023年 / 62卷
基金：
美国国家科学基金会;
关键词：
Gabor frames; Frame set; B-splines; GABOR FRAMES; DENSITY THEOREMS; ZAK TRANSFORMS; INTERPOLATION;
D O I：
10.1016/j.acha.2022.08.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：237 / 250
页数：14
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