Parseval frame wavelet multipliers in L 2(ℝ d )

Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L2(ℝd) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝd, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of existence of Schwartz class functions which are Parseval frame wavelets and approximate Parseval frame wavelet set wavelets does not easily generalize to higher dimensions. However, a construction of wavelet sets in [Formula: see text] which may be smoothed is presented. Finally, it is shown that a commonly used class of functions cannot be the result of convolutional smoothing of a wavelet set wavelet.

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Some Characterizations of Parseval Frame Wavelet

2009 International Conference on Computational Intelligence and Natural Computing ◽

10.1109/cinc.2009.15 ◽

2009 ◽

Author(s):

Guochang Wu ◽

Junmin Wang

Keyword(s):

Parseval Frame ◽

Parseval Frame Wavelet

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$L^{p}$-boundedness of wavelet multipliers

Hokkaido Mathematical Journal ◽

10.14492/hokmj/1285851914 ◽

2004 ◽

Vol 33 (3) ◽

pp. 637-645 ◽

Cited By ~ 6

Author(s):

Bolin MA ◽

M.W. WONG

Keyword(s):

Wavelet Multipliers

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

Nonlinear Engineering ◽

10.1515/nleng-2021-0004 ◽

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.

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