Scalar and vector tomography for the weighted transport equation with application to helioseismology
Thompson, Nathan L. and Bukhgeim, Alexander L.. "Scalar and vector tomography for the weighted transport equation with application to helioseismology" Journal of Inverse and Ill-posed Problems, vol. , no. , 2022. https://doi.org/10.1515/jiip-2021-0001
Motivated by the application to helioseismology, we demonstrate uniqueness and stability for a class of inverse problems of the weighted transport equation. Using A-analytic functions, this inverse problem is expressed as a Cauchy problem. In this form, we show that, for a finite even trigonometric polynomial weight function, the resulting system is well-conditioned numerically and permits a Carleman-like estimate with boundary terms.