Geodesic
Spectrum and Spectral Decomposition of a Non-Self-Adjoint Differential Operator
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 58-63.

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We obtain the spectrum structures and the spectral decomposition of a non-self-adjoint differential operator $L$ generated by the differential expression $l[y]\equiv-y''+\alpha x^me^{i\mu x}y$, $m,\mu\ge1$, in the space $L_2(-\infty,\infty)$.
Keywords: non-self-adjoint differential operator, spectral decomposition of an operator, the space $L_2(-\infty,\infty)$, resolvent of an operator, rational function, holomorphic continuation. 
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M. Dzh. Manafov. Spectrum and Spectral Decomposition of a Non-Self-Adjoint Differential Operator. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 58-63. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a6/

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