Trace formulas for Schrödinger operators on star graphs
We derive trace formulas of the Buslaev-Faddeev type for quantum star graphs. One of the new ingredients is high energy asymptotics of the perturbation determinant.
math-ph↗
arXiv subjects
Semra Demirel-Frank
Publications and source records attributed to Semra Demirel-Frank.
Sharp eigenvalue bounds on quantum star graphs
We prove that the optimal constant in the Lieb--Thirring inequality on a star graph with $N$ edges coincides with that on $\mathbb R$ if $N$ is even. For odd $N$ we show that this property holds when restricting to radial potentials and we prove an almost optimal bound for general potentials.
math.SP↗