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

Kamran Sadiq; Alexandru Tamasan

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arXiv · 2201.10926

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

Kamran Sadiq·Alexandru Tamasan

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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.

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Kamran Sadiq, Alexandru Tamasan. 2022-01-26. On the range of the planar $X$-ray transform on the Fourier lattice of the torus. https://arxiv.org/abs/2201.10926

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