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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 4, Pages 625-632
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 θE, 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 θE and f(x,y) is real analytic in 2 then it also extends to an entire function in 2.