On the range of the $ X $-ray transform of symmetric tensors compactly supported in the plane

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-09-19 DOI:10.3934/ipi.2022070

K. Sadiq, A. Tamasan

引用次数: 3

Abstract

A BSTRACT . We ﬁnd the 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 a symmetric tensor of compact support in the plane.

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在平面上紧支撑的对称张量的X射线变换的范围

摘要。我们确定了环面上函数g的傅立叶系数在平面上紧支撑对称张量的X射线变换范围内的充要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.