"On the frame set of the second-order B-spline" by A. Ganiou D. Atindehou, Christina Frederick et al.
 

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

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