Mathematics – Spectral Theory
Scientific paper
2009-07-31
Mathematics
Spectral Theory
25pages
Scientific paper
We show coincidence of the two definitions of the integrated density of states (IDS) for a class of relativistic Schroedinger 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-Ito formula for Levy processes. In addition, in case when both the magnetic field and the scalar potential are periodic, one also proves the existence of the IDS.
Iftimie Viorel
Mantoiu Marius
Purice Radu
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