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An Isaac Newton Institute Workshop

Quantum Graphs, their Spectra and Applications

Eigenvalue estimates for Schroedinger operators on regular metric trees

Author: Rupert Frank (Stockholm)

Abstract

We consider Lieb-Thirring and Cwikel-Lieb-Rozenblum inequalities for Schroedinger operators on regular metric trees. We give a necessary and sufficient condition for the validity of these inequalities in terms of the global growth of the tree. The behavior of these inequalities in the weak and strong coupling regime is discussed. The talk is based on joint work with T. Ekholm and H. Kovarik.