Higher Dimensional Continuous Wavelet Transform in Wiener Amalgam Spaces

2014 ◽  
pp. 747-768
Author(s):  
Ferenc Weisz
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Wiener Amalgam Spaces ◽  
Higher Dimensional ◽  
Amalgam Spaces

Convergence of the inverse continuous wavelet transform in Wiener amalgam spaces

Analysis ◽  
2015 ◽  
Vol 35 (1) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Fourier Transforms ◽  
Weak Sense ◽  
Continuous Wavelet ◽  
Norm Convergence ◽  
Wiener Amalgam Spaces ◽  
Summability Methods ◽  
Lebesgue Points ◽  
Amalgam Spaces

AbstractThe inversion formula for the continuous wavelet transform is usually considered in the weak sense. With the help of summability methods of Fourier transforms we obtain norm convergence and convergence at Lebesgue points of the inverse wavelet transform for functions from the

The continuous wavelet transform with rotations

2005 ◽  
Vol 4 (1) ◽  
pp. 45-55
Author(s):  
Jaime Navarro ◽  
Miguel Angel Alvarez
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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