Characterization of Sobolev spaces of arbitrary smoothness using nonstationary tight wavelet frames

2009 ◽  
Vol 172 (1) ◽  
pp. 371-398 ◽  
Author(s):  
Bin Han ◽  
Zuowei Shen
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Frames

scholarly journals Dualwavelet frames in Sobolev spaces on local fields of positive characteristic

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2091-2099
Author(s):  
Ishtaq Ahmad ◽  
Neyaz Sheikh
Keyword(s):  
Sobolev Spaces ◽  
Local Field ◽  
Positive Characteristic ◽  
Local Fields ◽  
Wavelet Frames ◽  
The Past ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Field Of Positive Characteristic

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

scholarly journals A Characterization of Multi-Wavelet Dual Frames in Sobolev Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Jianping Zhang ◽  
Jiajia Li
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Wavelet Frames ◽  
Dual Frames ◽  
The Past

For the past few years, wavelet and multi-wavelet frames have attracted interest from researchers. In this paper, we address some of these problems in the setting of the Sobolev space, and characterize of multi-wavelet dual frames in these spaces by using a pair of equations.

scholarly journals A characterization of wavelet convergence in sobolev spaces

2001 ◽  
Vol 78 (3-4) ◽  
pp. 271-324 ◽  
Author(s):  
Mark A. Kon ◽  
Louise Arakellan Rapha
Keyword(s):  
Sobolev Spaces

Nonuniform nonhomogeneous dual wavelet frames in Sobolev spaces in $$L^2({\mathbb {K}})$$

2020 ◽  
Vol 31 (7-8) ◽  
pp. 1145-1156 ◽  
Author(s):  
O. Ahmad ◽  
N. A. Sheikh ◽  
M. A. Ali
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Frames ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

scholarly journals Characterization of Orlicz Sobolev Spaces

2018 ◽  
Vol 10 (2) ◽  
pp. 104
Author(s):  
Tiziano Granucci
Keyword(s):  
Sobolev Spaces ◽  
Open Subset

We give a characterization of the Orlicz Sobolev spaces $W^{1,\Phi }\left(\Omega \right) $ when $\Omega \subset \mathbb{R} ^{N}$ is a open subset, $N\geq 1$ and $\Phi \in \triangle ^{2}$.

scholarly journals Nonhomogeneous Wavelet Dual Frames and Extension Principles in Reducing Subspaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jianping Zhang ◽  
Huifang Jia
Keyword(s):  
Wavelet Frames ◽  
Dual Frames ◽  
Reducing Subspaces ◽  
Extension Principles

It can be seen from the literature that nonhomogeneous wavelet frames are much simpler to characterize and construct than homogeneous ones. In this work, we address such problems in reducing subspaces of L2ℝd. A characterization of nonhomogeneous wavelet dual frames is obtained, and by using the characterization, an MOEP and an MEP are derived under general assumptions for such wavelet dual frames.

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