A diamagnetic inequality for semigroup differences

• Published in: Journal für die reine und angewandte Mathematik (Crelles Journal)
• Main Authors: Hundertmark, Dirk, Simon, Barry
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: De Gruyter 2004
• Subjects: laptev
• Online Access: https://doi.org/10.1515/crll.2004.036

The diamagnetic inequality for the magnetic Schrödinger semigroup is extended to the difference of the semigroups of magnetic Schrödinger operators with Neumann and Dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials A and potentials V. In particular, this bound renders moot all the technical issues in the recent proofs of the independence of the boundary conditions for the integrated density of states for magnetic Schrödinger operators: Independence of the boundary conditions for the free case, that is, for vanishing potentials and vector potentials, immediately implies independence of the boundary conditions of the integrated density of states for a large class of magnetic Schrödinger operators. © 2004 Walter de Gruyter Berlin; New York. Supported in part by NSF grants DMS-9707661 and DMS-0140592. It is a pleasure to thank Alexander Elgart for discussions and Hendrik Vogt for pointing us to [30]. D.H. also thanks Ari Laptev and Kjell-Ove Widman for their hospitality at the Mittag-Leffler institute. Published - 286.pdf Submitted - p286.pdf