Abstract
：
Recently, Gabor analysis on locally compact abelian (LCA) groups has interested some mathematicians. The half real line Double-struck capital R+=(0,infinity)$$ {\mathbb{R}}_{+}=\left(0,\infty \right) $$ is an LCA group under multiplication and the usual topology. This paper addresses spline Gabor frames for L2(Double-struck capital R+,d mu)$$ {L}<^>2\left({\mathbb{R}}_{+}, d\mu \right) $$, where mu$$ \mu $$ is the corresponding Haar measure. We introduce the concept of spline functions on Double-struck capital R+$$ {\mathbb{R}}_{+} $$ by mu$$ \mu $$-convolution and estimate their Gabor frame sets, that is, lattice sets such that spline generating Gabor systems are frames for L2(Double-struck capital R+,d mu)$$ {L}<^>2\left({\mathbb{R}}_{+}, d\mu \right) $$. For an arbitrary spline Gabor frame with special lattices, we present its one dual Gabor frame window, which has the same smoothness as the initial window function. For a class of special spline Gabor Bessel sequences, we prove that they can be extended to a tight Gabor frame by adding a new window function, which has compact support and same smoothness as the initial windows. And we also demonstrate that two spline Gabor Bessel sequences can always be extended to a pair of dual Gabor frames with the adding window functions being compactly supported and having the same smoothness as the initial windows.
Keyword
：
Gabor frame set
Gabor frame set
dual frame
dual frame
frame
frame
Gabor system
Gabor system
spline function
spline function
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| GB/T 7714 |
Yang, Ming
,
Li, Yun-Zhang
.
Spline function generating Gabor systems on the half real line
[J].
|
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
,
2023
,
46
(8)
: 9415-9441
.
|
| MLA |
Yang, Ming
等.
"Spline function generating Gabor systems on the half real line"
.
|
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
46
.
8
(2023)
: 9415-9441
.
|
| APA |
Yang, Ming
,
Li, Yun-Zhang
.
Spline function generating Gabor systems on the half real line
.
|
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
,
2023
,
46
(8)
, 9415-9441
.
|
| Export to |
NoteExpress RIS BibTex |
