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. 
@article{MZM_2007_82_1_a6,
     author = {M. Dzh. Manafov},
     title = {Spectrum and {Spectral} {Decomposition} of a {Non-Self-Adjoint} {Differential} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {58--63},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a6/}
}
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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/