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Christoph Schwerdt

Intrinsic ultracontractivity of Schrödinger semigroups in L2 (Rn)

Universität Rostock, 2024

https://doi.org/10.18453/rosdok_id00005172

Abstract: 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.

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