INJECTIVITY AND RANGE DESCRIPTION OF INTEGRAL MOMENT TRANSFORMS OVER m-TENSOR FIELDS IN Rn

被引：11

作者：

Mishra, Rohit Kumar ^{[1
]}

Sahoo, Suman Kumar ^{[2
]}

机构：

[1] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA

[2] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore, Karnataka, India

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2021年 / 53卷 / 01期

关键词：

ray transform; integral moment transforms; range characterization; inverse problems; John equation; tensor analysis; X-RAY TRANSFORM; MICROLOCAL ANALYSIS; DOPPLER TRANSFORM; SUPPORT THEOREMS; VECTOR FIELD; INVERSION; BEAM; RECONSTRUCTION; TOMOGRAPHY;

D O I：

10.1137/20M1347589

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a new decomposition result for rank m symmetric tensor fields which generalizes the well-known solenoidal and potential decomposition of tensor fields. This decomposition is then used to describe the kernel and prove an injectivity result for the first (k +1) integral moment transforms of symmetric m-tensor fields in R-n. Additionally, we present a range characterization for the first (k + 1) integral moment transforms in terms of the John equation.

引用

页码：253 / 278

页数：26

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