Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori
Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori
In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension~$n\geq 2$. We use them to derive Cwikel-Lieb-Rozenblum inequalities and and Lieb-Thirring inequalities for the number of negative eigenvalues of fractional Schroedinger operators on noncommutative tori in any dimension~$n\geq 2$. The latter leads to a Sobolev inequality for …