Research Paper#Mathematics, Dynamical Systems, Pseudodifferential Operators🔬 ResearchAnalyzed: Jan 3, 2026 16:14
Guillarmou's Normal Operator for Flows
Analysis
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.
Key Takeaways
- •Generalizes Guillarmou's normal operator to magnetic and thermostat flows.
- •Proves that the generalized normal operators are elliptic pseudodifferential operators of order -1.
- •Provides a stability estimate for the magnetic X-ray transform.
Reference
“The paper shows that generalized normal operators are elliptic pseudodifferential operators of order -1.”