Remarks on Counting Negative Eigenvalues of Schrödinger Operator on Regular Metric Trees


We discuss estimates on the number N − (HαV ) of negative eigenvalues of the Schrödinger operator HαV = −∆−αV on regular metric trees, as depending on the properties of the potential V ≥ 0 and on the value of the large parameter α. We obtain conditions on V guaranteeing the behavior N − (HαV ) = O(α ) for any given p ≥ 1/2. For a special class of trees we… (More)