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Non-self-adjoint Schrodinger operators A which correspond to non-symmetriczero-range potentials are investigated. For a given A, the description ofnon-real eigenvalues, spectral singularities and exceptional points areobtained; the possibility of interpretation of A as a self-adjoint operator ina Krein space is studied, the problem of similarity of A to a self-adjointoperator in a Hilbert space is solved.

Schrodinger Operators with Non-Symmetric Zero-Range Potentials