Helgason's support theorem for Radon transforms — A new proof and a generalization

1991 ◽  
pp. 1-5 ◽  
Author(s):  
Jan Boman
Keyword(s):  
Radon Transforms ◽  
Support Theorem

scholarly journals Extension sets for real analytic functions and applications to Radon transforms

1996 ◽  
Vol 19 (4) ◽  
pp. 625-632
Author(s):  
Vernor Arguedas ◽  
Ricardo Estrada
Keyword(s):  
Entire Function ◽  
Analytic Functions ◽  
Radon Transforms ◽  
Support Theorem ◽  
The Real ◽  
Real Analytic Functions ◽  
Small Set ◽  
Real Analytic

The real analytic character of a functionf(x,y)is determined from its behavior along radial directionsfθ(s)=f(scosθ,ssinθ)forθ∈E, whereEis a “small” set. A support theorem for Radon transforms in the plane is proved. In particular iffθextends to an entire function forθ∈Eandf(x,y)is real analytic inℝ2then it also extends to an entire function inℂ2.

Radon transforms on a class of cones with fixed axis direction

2005 ◽  
Vol 38 (37) ◽  
pp. 8003-8015 ◽  
Author(s):  
M K Nguyen ◽  
T T Truong ◽  
P Grangeat
Keyword(s):  
Radon Transforms ◽  
Axis Direction ◽  
Fixed Axis

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

scholarly journals Asymptotic support theorem for planar isotropic Brownian flows

2013 ◽  
Vol 41 (2) ◽  
pp. 699-721
Author(s):  
Moritz Biskamp
Keyword(s):  
Support Theorem
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