scholarly journals Ranges and Inversion Formulas for Spherical Mean Operator and Its Dual

1995 ◽  
Vol 196 (3) ◽  
pp. 861-884 ◽  
Author(s):  
M.M. Nessibi ◽  
L.T. Rachdi ◽  
K. Trimeche
Keyword(s):  
Spherical Mean Operator ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
And Inversion

scholarly journals Spaces ofDLptype and a convolution product associated with the spherical mean operator

2005 ◽  
Vol 2005 (3) ◽  
pp. 357-381 ◽  
Author(s):  
M. Dziri ◽  
M. Jelassi ◽  
L. T. Rachdi
Keyword(s):  
Harmonic Analysis ◽  
Dual Space ◽  
Convolution Product ◽  
Spherical Mean Operator ◽  
Spherical Mean

We define and study the spacesℳp(ℝ×ℝn),1≤p≤∞, that are ofDLptype. Using the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual spaceℳ′p(ℝ×ℝn)and describe its bounded subsets. Next, we define a convolution product inℳ′p(ℝ×ℝn)×Mr(ℝ×ℝn),1≤r≤p<∞, and prove some new results.

scholarly journals Besov-Hankel norms in terms of the continuous Bessel wavelet transform

2021 ◽  
Author(s):  
Ashish Pathak ◽  
Dileep Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Inversion Formulas ◽  
And Inversion

Using the theory of continuous Bessel wavelet transform in $L^2 (\mathbb{R})$-spaces, we established the Parseval and inversion formulas for the $L^{p,\sigma}(\mathbb{R}^+)$- spaces. We investigate continuity and boundedness properties of Bessel wavelet transform in Besov-Hankel spaces. Our main results: are the characterization of Besov-Hankel spaces by using continuous Bessel wavelet coefficient.

The vertical slice transform on the unit sphere

2019 ◽  
Vol 22 (4) ◽  
pp. 899-917 ◽  
Author(s):  
Boris Rubin
Keyword(s):  
Unit Sphere ◽  
Radon Transform ◽  
Integral Geometry ◽  
Singular Value ◽  
Hypersingular Integrals ◽  
Inversion Formulas ◽  
Spherical Mean ◽  
Singular Value Decompositions ◽  
Vertical Slice ◽  
Class Of Functions

Abstract The vertical slice transform in spherical integral geometry takes a function on the unit sphere Sn to integrals of that function over spherical slices parallel to the last coordinate axis. This transform was investigated for n = 2 in connection with inverse problems of spherical tomography. The present article gives a survey of some methods which were originally developed for the Radon transform, hypersingular integrals, and the spherical mean Radon-like transforms, and can be adapted to obtain new inversion formulas and singular value decompositions for the vertical slice transform in the general case n ≥ 2 for a large class of functions.

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