On the range of the planar X-ray transform on the Fourier lattice of the torus

2022/01/26 by Sadiq, Kamran, Tamasan, Alexandru
#35J56 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 44A12 #Secondary 45E05

paper · doi:10.48550/arxiv.2201.10926

Abstract

We find necessary and sufficient conditions on the Fourier coefficients of a function g on the torus to be in the range of the X-ray transform of functions with compact support in the plane, and establish the connection between the range characterization based on the Bukhgeim-Hilbert transform and the classical Gelfand-Graev, Helgason, and Ludwig characterization.

Related

• On the range of the X-ray transform of symmetric tensors compactly supported in the plane
• A question about the Fourier transform
• The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations
• Restriction of the Fourier transform to some oscillating curves
• Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces