On the absence of positive eigenvalues of Schrödinger operators with rough potentials

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Eigenvalue bounds for Schrödinger operators with complex potentials. II (2015, methodology): “) We include our proof of (C) since it is much simpler than the arguments in [14, 17] and since the same reasoning will give the assertion in (B) for E 2 Œ0;1/ where the results of [17] are not applicable.”
A limiting absorption principle for the three-dimensional Schrödinger equation with Lp potentials (2004, methodology): “They further conjectured that their main result (Theorem 2.1 in [ IonJer ]) remains valid for potentials V 2 L2(R3).”
Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials (2007, result): “Thus we are in the framework of the standard Agmon theory and we deduce that λ is an eigenvalue of −∆ + b(x); but this is excluded under our assummtions on b, for instance by the results of[22] (Theorem 2.”