The Scattering Resonances for Schrödinger-Type Operators with Unbounded Potentials

.This paper addresses the meromorphic continuation of the outgoing resolvent associated with Schrödinger-type operators in three dimensions. The first part focuses on the classical Schrödinger-type operator involving unbounded potentials. The absence of nonzero real poles for the outgoing resolvent is investigated. The second part examines the fractional Schrödinger operator, including both bounded and unbounded potentials. The analysis relies on a resolvent identity that establishes a connection between the resolvents of the fractional Schrödinger operator and its classical counterpart.Keywordsscattering resonancesSchrödinger operatorfractional Schrödinger operatorunbounded potentialsmeromorphic continuationresolvent estimatesMSC codes35P2547A1047A40