- 09-128 Viorel Iftimie, Marius Mantoiu and Radu Purice
- Unicity of the Integrated Density of States for Relativistic Schr dinger Operators with Regular Magnetic Fields and Singular Electric Potentials
Jul 31, 09
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Abstract. We show coincidence of the two definitions of the integrated density of states (IDS) for a class of relativistic Schr dinger operators with magnetic fields and scalar potentials, the first one relying on the eigenvalue counting function of operators induced on open bounded sets with Dirichlet boundary conditions, the other one involving the spectral projections of the operator defined on the entire space. In this way one generalizes previous results for non-relativistic operators. The proofs needs the magnetic pseudodifferential calculus, as well as a Feynman-Kac-It formula for L vy processes. In addition, in case when both the magnetic field and the scalar potential are periodic, one also proves the existence of the IDS.