Curved version of Radon's inversion formula on the plane. (15th December 2017)

• Record Type: Journal Article
• Authors: Gindikin, Simon
• Is Part Of: Inverse problems. Volume 34:Number 1(2018:Jan.)
• Publication Date: 2017-12-15
• Subjects: Radon transform -- characteristic set -- horocycles; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa8d92
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We extend Radon's inversion formula for lines on the plane up to a closed differential 1-form on the set of plane curves, which expresses a function at a point through the integrals along the curves of some differential operators of this function. We consider characteristic families of curves for which functions can be reconstructed through integrals along curves of the family using our inversion formula. We verify that the families of affine lines and of hyperbolic horocycles are characteristic.