Weighted matrix integral geometry (Q5932600)

\textit{R. G. Mukhometov} [Sov. Math., Dokl. 18, 27--31 (1977; Zbl 0372.53034) and Mat. Probl. Geofiz. 6, 2, 212-242 (1975; Zbl 0371.53051)] obtained uniqueness results and stability estimates for solutions to the following weighted integral geometry problem: Given a simply connected plane domain \(D\) with smooth boundary and a regular family of curves in \(D\), determine an unknown scalar function from its weighted integrals along the curves of this regular family. The article under review extends these uniqueness results and stability estimates to the case of unknown \(n\times n\) matrix functions.