scholarly journals Characterization of nonhomogeneous dual wavelet frames in Sobolev spaces

ScienceAsia ◽  
2022 ◽  
Vol 48 (1) ◽  
pp. 101
Author(s):  
Jian-Ping Zhang ◽  
Qiang-Qiang Chang
Keyword(s):  
Sobolev Spaces ◽  
Wavelet Frames ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

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.

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

The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions

2010 ◽  
Vol 439-440 ◽  
pp. 1135-1140
Author(s):  
Jun Qiu Wang ◽  
Jian Guo Wang
Keyword(s):  
Scaling Functions ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
The Past ◽  
Single Function ◽  
Dual Wavelet Frames ◽  
Popular Subject ◽  
Compactly Supported Functions ◽  
Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

Construction of approximate dual wavelet frames

2013 ◽  
Vol 40 (1) ◽  
pp. 273-282 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Darian M. Onchis ◽  
Christoph Wiesmeyr
Keyword(s):  
Wavelet Frames ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

COMPACTLY SUPPORTED MULTIVARIATE, PAIRS OF DUAL WAVELET FRAMES OBTAINED BY CONVOLUTION

2008 ◽  
Vol 06 (02) ◽  
pp. 183-208 ◽  
Author(s):  
MARTIN EHLER
Keyword(s):  
Approximation Order ◽  
Refinable Functions ◽  
Wavelet Frames ◽  
Refinable Function ◽  
Vanishing Moments ◽  
Wavelet System ◽  
Compactly Supported ◽  
Mask Size ◽  
Dual Wavelet Frames ◽  
Dual Wavelet

In this paper, we present a construction of compactly supported multivariate pairs of dual wavelet frames. The approach is based on the convolution of two refinable distributions. We obtain smooth wavelets with any preassigned number of vanishing moments. Their underlying refinable function is fundamental. In the examples, we obtain symmetric wavelets with small support from optimal refinable functions, i.e. the refinable function has minimal mask size with respect to smoothness and approximation order of its generated multiresolution analysis. The wavelet system has maximal approximation order with respect to the underlying refinable function.

Weak nonhomogeneous wavelet dual frames for Walsh reducing subspace of L2(ℝ+)

2021 ◽  
pp. 2150040
Author(s):  
Yan Zhang ◽  
Yun-Zhang Li
Keyword(s):  
Extension Principle ◽  
Transform Domain ◽  
Wavelet Frames ◽  
Dual Frames ◽  
Reducing Subspace ◽  
Reducing Subspaces ◽  
Extension Principles ◽  
Dual Wavelet Frames ◽  
Dual Wavelet ◽  
Fourier Transform Domain

In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].

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