Extension sets for real analytic functions and applications to Radon transforms (Q1922837)

Summary: The real analytic character of a function \(f(x,y)\) is determined from its behavior along radial directions \(f_\theta(s)= f(s\cos\theta, s\sin \theta)\) for \(\theta\in E\), where \(E\) is a ``small'' set. A support theorem for Radon transforms in the plane is proved. In particular, if \(f_\theta\) extends to an entire function for \(\theta\in E\) and \(f(x,y)\) is real analytic in \(\mathbb{R}^2\) then it also extends to an entire function in \(\mathbb{C}^2\).