Geodesic
Some spectral relations
Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 561-568 
A. A. Stakun. Some spectral relations. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 561-568. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a8/
@article{MZM_1975_18_4_a8,
     author = {A. A. Stakun},
     title = {Some spectral relations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {561--568},
     year = {1975},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a8/}
}
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UR  - http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a8/
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ID  - MZM_1975_18_4_a8
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the zeta function of a second-order differential operator which has a second-order turning point: $$ Lu=\frac{d^2u}{dx^2}+[\lambda^2q(x)+R(x)]u, $$ where $q(x)=x^2q_1(x)$, $q_1(x)\ne0$ and $u(0)=u(1)=0$. We construct an asymptotic series and calculate regularized traces for the eigenvalues of this operator.