Geodesic
The inverse problem for a class of ordinary differential operators with periodic coefficients
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 1, pp. 114-121 
R. F. Efendiev. The inverse problem for a class of ordinary differential operators with periodic coefficients. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 1, pp. 114-121. http://geodesic.mathdoc.fr/item/JMAG_2004_11_1_a6/
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     author = {R. F. Efendiev},
     title = {The inverse problem for a class of ordinary differential operators with periodic coefficients},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {114--121},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2004_11_1_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The direct and inverse problem of spectral analyses of a class of ordinary differential equations of order $2m$ with coefficients polynomially depending on the spectral parameter are investigated. It is shown that, the spectrum of the operator pencil is continuous, fill in the rays $\{k\omega_j/\, 0\le k<\infty,\ j=\overline{0,2m-1}\}$, $\omega_j=\exp\left(\frac{ij\pi}{m}\right)$, and there exist spectral singularities on the continues spectrum which coincide with the numbers $\frac{n\omega_j}2$, $j=\overline{0,2m-1}$, $n=1,2,\dots$ The inverse problem of reconstructing of the coefficients by generalized normalizing numbers is solved.