Scattering theory for repulsive Schrödinger operators and applications to limit circle problem

Abstract

In this note, we study existence of the outgoing/incoming resolvents of repulsive Schrödinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, we recover the classical result: The repulsive Schroödinger operators with large repulsive constant is not essentially self-adjoint on the Schwartz space.

20pages

References in corpus (2)

• Upper bound on the density of Ruelle resonances for Anosov flows
• Scattering theory for the Schrodinger equation with repulsive potential

Cited by in corpus (1)

• Equivalence of classical and quantum completeness for real principal type operators on the circle