Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^2({\mathbb{R}}^n)$ by Logarithmic Sobolev inequalities

Christoph Schwerdt, Alexander Mill, Dirk Hundertmark

In the first part of this article we present a growth condition on the potential $q$ in the Schrödinger operator $H=-\Delta +q(x)$ in ${\mathrm{L}}^2\left({\mathbb{R}}^n\right)$ that…