10.18453/rosdok_id00005172 Schwerdt, Christoph Christoph Schwerdt http://d-nb.info/gnd/1392850894 Universität Rostock 2024 510 Mathematics 2024 en https://purl.uni-rostock.de/rosdok/id00005172 urn:nbn:de:gbv:28-rosdok_id00005172-6 A possible intrinsic ultracontractivity of the magnetic Schrödinger semigroups was investigated. Usually, Rosen inequalities are essential for intrinsic ultracontractivity but hard to find since a specific asymptotical behaviour of the ground state is required. However, in the magnetic case operators of the Schrödinger semigroup are no longer positivity improving. This causes a variety of problems including the use of Logarithmic Sobolev inequalities. Using diamagnetic inequalities quasi intrinsic ultracontractivity was shown in the magnetic case.