Intrinsic ultracontractivity for Schrödinger semigroups based on cylindrical fractional Laplacian on the plane

Tadeusz Kulczycki, Kinga Sztonyk

We study Schrödinger operators on ${\mathbb{R}}^2$ $$H={\left(-\frac{{\partial }^2}{\partial x_1^2}\right)}^{\alpha /2}+{\left(-\frac{{\partial }^2}{\partial x_2^2}\right)}^{\alpha /2}+V,$$ for $α…