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

scholarly journals Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Fourier Transforms ◽  
Lebesgue Point ◽  
Strong Summability ◽  
Wiener Amalgam Spaces ◽  
Wiener Amalgam Space ◽  
Almost Everywhere ◽  
Lebesgue Points ◽  
Amalgam Spaces

We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, iffis in the Wiener amalgam spaceW(L1,lq)(R)andfis almost everywhere locally bounded, orf∈W(Lp,lq)(R)  (1<p<∞,1≤q<∞), then strongθ-summability holds at each Lebesgue point off. The analogous results are given for Fourier series, too.

INVERSION OF THE RADON TRANSFORM ASSOCIATED WITH THE CLASSICAL DOMAIN OF TYPE ONE

2005 ◽  
Vol 16 (08) ◽  
pp. 875-887 ◽  
Author(s):  
JIANXUN HE ◽  
HEPING LIU
Keyword(s):  
Wavelet Transform ◽  
Differential Operator ◽  
Lie Group ◽  
Radon Transform ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Weak Sense ◽  
Continuous Wavelet ◽  
Nilpotent Lie Group ◽  
Classical Domain

Let D(Ω,Φ) be the unbounded realization of the classical domain [Formula: see text] of type one. In general, its Šilov boundary [Formula: see text] is a nilpotent Lie group of step two. In this article we define the Radon transform on [Formula: see text], and obtain an inversion formula [Formula: see text] in terms of a determinantal differential operator. Moreover, we characterize a subspace of [Formula: see text] on which the Radon transform is a bijection. By use of the suitable continuous wavelet transform we establish a new inversion formula of the Radon transform in weak sense without the assumption of differentiability.

Sign in / Sign up

Export Citation Format

Share Document