In previous articles, a magnetic pseudodifferential calculus and a family of -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 -behavior modeled by an abelian -algebra. Some of these classes generate -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.
Cite this article
Max Lein, Marius Măntoiu, Serge Richard, Magnetic Pseudodifferential Operators with Coefficients in -Algebras. Publ. Res. Inst. Math. Sci. 46 (2010), no. 4, pp. 755–788DOI 10.2977/PRIMS/25