Geodesic
Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators
Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 401-408.

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Conditions are found under which $A^1\in\sigma_p$ ($A$ is a nonself-adjoint operator). For differential operators in $L_2(-\infty, \infty)$ with real coefficients, conditions are found for the existence of a regular point, necessary and sufficient and also sufficient conditions are found for the spectrum to be discrete, and conditions are found for the system of characteristic and associated vectors to be complete. 
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     author = {I. I. Golichev},
     title = {Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--408},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a4/}
}
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I. I. Golichev. Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators. Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 401-408. http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a4/