关于环面Fourier格上平面$X$射线变换的范围
On the range of the planar $X$-ray transform on the Fourier lattice of the torus
摘要：
我们找到了环面上函数$g$的傅里叶系数在平面上紧支集函数的$X$射线变换范围内的充要条件，并建立了基于Bukhgeim-希尔伯特变换的范围刻画与经典的Gelfand-Graev，Helgason和Ludwig刻画之间的联系.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
