Extension sets for real analytic functions and applications to Radon transforms

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.