Magnetic Pseudodifferential Operators with Cofficients in C-Algebras

Abstract

In previous articles, a magnetic pseudodifferential calculus and a family of C-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol classes of Hörmander type with an x-behavior modeled by an abelian C-algebra. Some of these classes generate C-algebras associated with the twisted dynamical system.We show the relevance of these classes to the spectral analysis of pseudodifferential operators with anisotropic symbols and magnetic fields.