On the Angular Moment Operators of Attenuated Ray Transforms of Scalar \(\boldsymbol {3D}\) -Fields

Under consideration are the operators of angular moments which map the values of generalized attenuated ray transforms (ART) into the set of symmetric \(p \)-tensor fields. The differential relations between the values of ARTs of various orders, acting on stationary or dynamic source distributions \(f \), serve as the basis for establishing the differential connections between the tensor fields of angular moments of various orders \(k \) and ranks \(p \). The particular cases are indicated allowing us to obtain some previously known results. Connections of the ARTs of order \(k \) with the problems of tomography and integral geometry as well as the established properties and connections between ARTs and angular moments can be useful as additional information when constructing the iterative algorithms for solving the problems of dynamic refraction tensor tomography.