Geodesic
Trace formulas in the case of the Orr--Sommerfeld equation
Izvestiya. Mathematics , Tome 2 (1968) no. 3, pp. 585-600.

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We introduce a $\zeta$-function associated with the spectrum of the Orr–Sommerfeld equation; we also compute regularized sums of positive integral powers of eigenvalues of a boundary value problem. 
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V. B. Lidskii; V. A. Sadovnichii. Trace formulas in the case of the Orr--Sommerfeld equation. Izvestiya. Mathematics , Tome 2 (1968) no. 3, pp. 585-600. http://geodesic.mathdoc.fr/item/IM2_1968_2_3_a5/

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