Some Characterizations of Parseval Frame Wavelet

2009 ◽  
Author(s):  
Guochang Wu ◽  
Junmin Wang
Keyword(s):  
Parseval Frame ◽  
Parseval Frame Wavelet

SMOOTH PARSEVAL FRAMES FOR L2(ℝ) AND GENERALIZATIONS TO L2(ℝd)

2013 ◽  
Vol 11 (06) ◽  
pp. 1350047
Author(s):  
EMILY J. KING
Keyword(s):  
Higher Dimensions ◽  
Wavelet Sets ◽  
Parseval Frame ◽  
Wavelet Set ◽  
Parseval Frames ◽  
Schwartz Class ◽  
Frame Wavelets ◽  
Class Of Functions ◽  
Parseval Frame Wavelet ◽  
Provided Examples

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.

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.

scholarly journals Characterizations of Irregular Multigenerator Gabor Frame on Periodic Subsets of ℝ

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
D. H. Yuan ◽  
Y. Feng ◽  
Y. F. Shen ◽  
S. Z. Yang
Keyword(s):  
Necessary Conditions ◽  
Gabor Frame ◽  
Frame Theory ◽  
Parseval Frame

We consider the multigenerator system{EmblTnalφl,m,n∈ℤ,l=0,…,r-1}forφ0,…,φr-1∈L2(𝕊)anda0,b0,…,ar-1,br-1>0, where the parametersb0,…,br-1>0are not necessary the same. With the help of frame theory, we provide some sufficient or necessary conditions for the system to be a frame forL2(𝕊). Moreover, we present some characterizations for this system to be a Parseval frame.

scholarly journals Optimal shift invariant spaces and their Parseval frame generators

2007 ◽  
Vol 23 (2) ◽  
pp. 273-283 ◽  
Author(s):  
Akram Aldroubi ◽  
Carlos Cabrelli ◽  
Douglas Hardin ◽  
Ursula Molter
Keyword(s):  
Parseval Frame ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

scholarly journals NECESSARY AND SUFFICIENT CONDITIONS FOR PRIME PARSEVAL FRAMES

2017 ◽  
Vol 18 (6) ◽  
pp. 42-48
Author(s):  
I.S. Ryabtsov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Parseval Frame ◽  
Parseval Frames ◽  
Necessary And Sufficient

In the article we consider two disjoint classes of frames, prime and composite Parseval frames, the union of which forms a set of Parseval frames. The main goal is to obtain a description of these two classes. In this article we prove necessary and sufficient conditions for the frame to be a prime Parseval frame.

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