The generalized Saint Venant operator and integral moment transforms

Mishra, Rohit; Sahoo, Suman

doi:10.1090/proc/16080

The generalized Saint Venant operator and integral moment transforms
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by Rohit Kumar Mishra and Suman Kumar Sahoo

Proc. Amer. Math. Soc. 151 (2023), 189-199

DOI: https://doi.org/10.1090/proc/16080

Published electronically: August 18, 2022

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Abstract:

In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov [Inverse and ill-posed problems series, VSP, Utrecht, 1994] to describe the kernel of the integral moment transforms over symmetric $m$-tensor fields in $n$-dimensional Euclidean space. We also provide an equivalence between the injectivity question for the integral moment transforms and generalized Saint Venant operator over symmetric tensor fields of Schwartz class.

References

Anuj Abhishek and Rohit Kumar Mishra, Support theorems and an injectivity result for integral moments of a symmetric $m$-tensor field, J. Fourier Anal. Appl. 25 (2019), no. 4, 1487–1512. MR 3977125, DOI 10.1007/s00041-018-09649-7
Sombuddha Bhattacharyya, Local uniqueness of the density from partial boundary data for isotropic elastodynamics, Inverse Problems 34 (2018), no. 12, 125001, 10. MR 3861940, DOI 10.1088/1361-6420/aade76
Sombuddha Bhattacharyya, Venkateswaran P. Krishnan, and Suman Kumar Sahoo, Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data, arXiv:2111.07610, 2021
Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo, and Vladimir A. Sharafutdinov, Momentum ray transforms, Inverse Probl. Imaging 13 (2019), no. 3, 679–701. MR 3959332, DOI 10.3934/ipi.2019031
Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo, and Vladimir A. Sharafutdinov, Momentum ray transforms, II: range characterization in the Schwartz space, Inverse Problems 36 (2020), no. 4, 045009, 33. MR 4075194, DOI 10.1088/1361-6420/ab6a65
Rohit Kumar Mishra and Suman Kumar Sahoo, Injectivity and range description of integral moment transforms over $m$-tensor fields in $\Bbb {R}^n$, SIAM J. Math. Anal. 53 (2021), no. 1, 253–278. MR 4198570, DOI 10.1137/20M1347589
V. A. Sharafutdinov, A problem of integral geometry for generalized tensor fields on $\textbf {R}^n$, Dokl. Akad. Nauk SSSR 286 (1986), no. 2, 305–307 (Russian). MR 823390
V. A. Sharafutdinov, Integral geometry of tensor fields, Inverse and Ill-posed Problems Series, VSP, Utrecht, 1994. MR 1374572, DOI 10.1515/9783110900095