Extension sets for real analytic functions and applications to Radon transforms. (1996)

• Record Type: Journal Article
• Authors: Arguedas, Vernor; Estrada, Ricardo
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 19:Number 4(1996)
• Page Start: 625
• Page End: 632
• Publication Date: 1996
• Subjects: Real-analytic functions -- real analytic functions of exponential type -- Radon transform; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171296000889
• Languages: English
• ISSNs: 0161-1712

Abstract

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 .