Scattering theory for repulsive Schr\"odinger operators and applications to limit circle problem.
2019
In this note, we study existence of the outgoing/incoming resolvents of repulsive Schr\"odinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, we recover the classical result: The repulsive Schro\"odinger operators with large repulsive constant is not essentially self-adjoint on the Schwartz space.
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