Magnetic pseudodifferential operators with coefficients in C*-algebras

TL;DR

This paper extends magnetic pseudodifferential calculus to include symbol classes modeled by abelian C*-algebras, linking them to spectral analysis of operators with magnetic fields.

Contribution

It introduces new symbol classes of Hörmander type within the magnetic pseudodifferential framework, connecting them to associated C*-algebras and spectral analysis.

Findings

Extended formalism to include x-behavior modeled by abelian C*-algebras

Generated C*-algebras related to twisted dynamical systems

Relevance demonstrated for spectral analysis of magnetic pseudodifferential operators

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 H\"ormander type with an x-behavior modelized 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.