ピカール原理に関する除外摂動の十分条件

概要

論文の詳細を見る
With a Schrodinger operator -Δ+μ on the punctured unit disc having a rotationally invariant signed measure μ as its potential we associate another Schrodinger operator -Δ+(μ+v) having the measure μ+v obtained from μ by applying a small perturbation +v, which is also a rotationally invariant signed measure, as its potential. The above measure v is referred to as a negligible perturbation for the Picard principle if the Picard principle is valid or invalid simultaneously for the operator -Δ+μ and -Δ+(μ+v) for every admissible μ. To characterize negligible perturbations is very important especially from the view point of many practical applications and actually quite a few such conditions and mostly sufficient conditions have been given by many authors. We will give in the present paper an entirely new and in a sense more precise sufficient condition for a given v to be negligible compared with those known thus far.