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

页码：237 / 250

页数：14

共 50 条

[21] B-SPLINE LEVEL SET FOR DROSOPHILA IMAGE SEGMENTATION
Rahali, Rim
Ben Salem, Yassine
Dridi, Noura
Dahman, Hassen
2020 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP), 2020, : 413 - 417
[22] Extended cubic uniform B-spline and α-B-spline
Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Zidonghua Xuebao, 2008, 8 (980-983):
[23] Static polarizabilities of hydrogen in the B-spline basis set
Bhatti, Mohammad I.
Coleman, Kevin D.
Perger, Warren F.
Physical Review A - Atomic, Molecular, and Optical Physics, 2003, 68 (4 B): : 1 - 044503
[24] B-spline tight frame based force matching method
Yang, Jianbin
Zhu, Guanhua
Tong, Dudu
Lu, Lanyuan
Shen, Zuowei
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 362 : 208 - 219
[25] A new cubic B-spline method for approximating the solution of a class of nonlinear second-order boundary value problem with two dependent variables
Lang, Feng-Gong
Xu, Xiao-Ping
SCIENCEASIA, 2014, 40 (06): : 444 - 450
[26] A quadratic trigonometric B-Spline as an alternate to cubic B-spline
Samreen, Shamaila
Sarfraz, Muhammad
Mohamed, Abullah
ALEXANDRIA ENGINEERING JOURNAL, 2022, 61 (12) : 11433 - 11443
[27] Solution of Second Order Singular Perturbed Delay Differential Equation Using Trigonometric B-Spline
Vaid, Mandeep Kaur
Arora, Geeta
INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES, 2019, 4 (02) : 349 - 360
[28] alpha B-spline: A linear singular blending B-spline
Loe, KF
VISUAL COMPUTER, 1996, 12 (01): : 18 - 25
[29] Second-Order Logic and Set Theory
Vaananen, Jouko
PHILOSOPHY COMPASS, 2015, 10 (07): : 463 - 478
[30] NUMERICAL SOLUTION FOR A CLASS OF FRACTIONAL VARIATIONAL PROBLEM VIA SECOND ORDER B-SPLINE FUNCTION
Ismail, Noratiqah Farhana Binti
Phang, Chang
JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY, 2019, 25 (03) : 171 - 182

← 1 2 3 4 5 →