Magnetic pseudodifferential operators with coefficients in C∗-algebras

M. Lein (1) , Marius Mantoiu (2) , Serge Richard (3)

1 Zentrum Mathematik, Department m5
2 Departamento de Matematicas
3 ICJ - Institut Camille Jordan

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 Hoermander 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.

Mots clés: Magnetic field; pseudodifferential operator; C*-algebras; affiliation; essential spectrum; symbol class; twisted crossed-product

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

M. Lein, Marius Mantoiu, Serge Richard. Magnetic pseudodifferential operators with coefficients in C∗-algebras. Publ. RIMS, Kyoto Univ., 2010, 46, pp.755 - 788. ⟨hal-00355982⟩