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The ray transform associates to functions and more generally symmetric tensor fields, integrals along straight lines in \(\mathbb {R}^n\) . The momentum ray transform (MRT), introduced by Sharafutdinov, generalizes this by using polynomial-type weight functions. This chapter surveys recent developments in the study of MRT and gives its applications in the resolution of uniqueness results for higher order versions of the Calderón inverse problem. This overview is mainly based on the works of Bhattacharyya et al. (SIAM J. Math. Anal. 55(4):4000–4038, 2023); Sahoo, and Salo (J. Differ. Equ. 360:407–451, 2023); and Bhattacharyya et al. (Inverse problems for third-order nonlinear perturbations of biharmonic operators. arXiv:2312.07985, 2023).

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Applications of Momentum Ray Transforms in Inverse Problems

  • 会议论文

  • 发表日期：

    2025年

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  • Venkateswaran P. Krishnan,
  • Suman Kumar Sahoo

摘要

The ray transform associates to functions and more generally symmetric tensor fields, integrals along straight lines in \(\mathbb {R}^n\) . The momentum ray transform (MRT), introduced by Sharafutdinov, generalizes this by using polynomial-type weight functions. This chapter surveys recent developments in the study of MRT and gives its applications in the resolution of uniqueness results for higher order versions of the Calderón inverse problem. This overview is mainly based on the works of Bhattacharyya et al. (SIAM J. Math. Anal. 55(4):4000–4038, 2023); Sahoo, and Salo (J. Differ. Equ. 360:407–451, 2023); and Bhattacharyya et al. (Inverse problems for third-order nonlinear perturbations of biharmonic operators. arXiv:2312.07985, 2023).