International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 625-632
doi:10.1155/S0161171296000889
Extension sets for real analytic functions and applications to Radon transforms
Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica
Received 23 November 1994
Copyright © 1996 Vernor Arguedas and Ricardo Estrada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The real analytic character of a function f(x,y) is determined from its behavior along
radial directions fθ(s)=f(scosθ,ssinθ) for θ∈E, where E is a “small” set. A support theorem for
Radon transforms in the plane is proved. In particular if fθ extends to an entire function for θ∈E and
f(x,y) is real analytic in ℝ2 then it also extends to an entire function in ℂ2.