Extension sets for real analytic functions and applications to Radon transforms. (1996) - Arguedas, Vernor; Estrada, Ricardo
Abstract : The real analytic character of a functionf ( x, y ) is determined from its behavior along radial directionsf θ ( s ) = f ( s cos θ, s sin θ ) forθ ∈ E, whereE is a small set. A support theorem for Radon transforms in the plane is proved. In particular iff θ extends to an entire function forθ ∈ E andf ( x, y ) is real analytic inℝ 2 then it also extends to an entire function inℂ 2 .