#### Vol. 14, No. 7, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Scattering theory for repulsive Schrödinger operators and applications to the limit circle problem

### Kouichi Taira

Vol. 14 (2021), No. 7, 2101–2122
##### Abstract

We study existence of the outgoing/incoming resolvents of repulsive Schrödinger operators which may not be essentially self-adjoint on the Schwartz space. As a consequence, we construct ${L}^{2}$-eigenfunctions associated with complex eigenvalues by a standard technique of scattering theory. In particular, we give another proof of the classical result via microlocal analysis: the repulsive Schrödinger operators with large repulsive exponent are not essentially self-adjoint on the Schwartz space.