scholarly journals Wavelet frames for distributions; local and pointwise regularity

2003 ◽  
Vol 154 (1) ◽  
pp. 59-88 ◽  
Author(s):  
Hans Triebel
Keyword(s):  
Wavelet Frames ◽  
Pointwise Regularity

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

A novel approach on micropolar fluid flow in a porous channel with high mass transfer via wavelet frames

2021 ◽  
Vol 10 (1) ◽  
pp. 39-45
Author(s):  
S. Kumbinarasaiah ◽  
K.R. Raghunatha
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
High Mass ◽  
Porous Channel ◽  
Physical Parameters ◽  
Wavelet Frames ◽  
Parseval Frame ◽  
Highly Nonlinear ◽  
Frame Method

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

2014 ◽  
Vol 57 (2) ◽  
pp. 254-263 ◽  
Author(s):  
Ole Christensen ◽  
Hong Oh Kim ◽  
Rae Young Kim
Keyword(s):  
Extension Principle ◽  
Sufficient Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Number Of Generators ◽  
Unitary Extension

AbstractThe unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

scholarly journals Unitary Extension Principle for Nonuniform Wavelet Frames in L2(ℝ)

2021 ◽  
Vol 17 (1) ◽  
pp. 79-94
Author(s):  
Hari Krishan Malhotra ◽  
◽  
Lalit Kumar Vashisht ◽  
Keyword(s):  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension

scholarly journals Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

scholarly journals Multivariate Wavelet Frames

2016 ◽  
Author(s):  
Maria Skopina ◽  
Aleksandr Krivoshein ◽  
Vladimir Protasov
Keyword(s):  
Wavelet Frames
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