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The classification of solutions for some dissipative systems by the information of the spectrum is established. Its generator is non self-adjoint Schrö dinger operator with rank one singular perturbation. For the proof, a generalized Parseval formula is constructed. 2000 Mathematics Subject Classification. 35P10, 35P25, 81Q10, 81Q15doi:10.32917/hmj/1150998510 fatcat:sj6rfide35ft5n4jrbjhliioim