Commutator Criteria for Magnetic Pseudodifferential Operators

TL;DR

This paper establishes intrinsic commutator-based criteria for identifying magnetic pseudodifferential operators, facilitating analysis of their properties without dependence on vector potentials.

Contribution

It introduces intrinsic commutator criteria for magnetic pseudodifferential operators, independent of vector potential choices, advancing the theoretical framework.

Findings

Criteria for magnetic pseudodifferential operators established

Applications to inversion, functional calculus, and evolution groups

Results are independent of vector potential choices

Abstract

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.