Commutator Criteria for Magnetic Pseudodifferential Operators

Understand

The gauge covariant magnetic Weyl calculus has been introduced and studied in previous works.

• We prove criteria in terms of commutators for operators to be magnetic pseudo-differential operators of suitable symbol classes.
• The approach is completely intrinsic; neither the statements nor the proofs depend on a choice of a vector potential.
• We apply this criteria to inversion problems, functional calculus, affiliation results and to the study of the evolution group generated by a magnetic pseudo-differential operator.