Guillarmou's Normal Operator for Flows

This paper extends Guillarmou's normal operator, a tool analogous to the geodesic X-ray transform's normal operator, to magnetic and thermostat flows. The key result is demonstrating that these generalized normal operators are elliptic pseudodifferential operators of order -1, leading to a stability estimate for the magnetic X-ray transform. This work contributes to the mathematical understanding of these complex dynamical systems and provides a stability result for a related transform.