scholarly journals Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform

1983 ◽  
Vol 95 (2) ◽  
pp. 437-448 ◽  
Author(s):  
Eric Todd Quinto
Keyword(s):  
Radon Transform ◽  
Singular Value ◽  
Inversion Methods ◽  
Singular Value Decompositions ◽  
And Inversion

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.

scholarly journals Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators

2001 ◽  
Vol 8 (2) ◽  
pp. 323-332
Author(s):  
A. Meskhi
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators ◽  
Integral Transforms ◽  
Singular Value ◽  
Entropy Numbers ◽  
Liouville Type ◽  
Singular Value Decompositions

Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.

scholarly journals Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs

2019 ◽  
Vol 51 (6) ◽  
pp. 4356-4381 ◽  
Author(s):  
Giovanni S. Alberti ◽  
Francesca Bartolucci ◽  
Filippo De Mari ◽  
Ernesto De Vito
Keyword(s):  
Radon Transform ◽  
Dual Pairs ◽  
And Inversion
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