Retraction Note: Minimally thin sets associated with the stationary Schrödinger operator

This article has been retracted. Please see the Retraction Notice for more detail: 10.1186/s13660-021-02575-1

GENERALIZATION OF THE PHRAGMÉN–LINDELÖF THEOREMS FOR SUBFUNCTIONS

In this paper, we consider the Phragmén–Lindelöf theorem for subfunctions, associated with the stationary Schrödinger operator. Meanwhile, the integral representations and a-harmonic majorants of them are also given.

Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone

We give some criteria fora-minimally thin sets anda-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside ana-rarefied set. Finally we illustrate the relation between thea-minimally thin set and thea-rarefied set in a cone.