The inverse problem for a class of ordinary differential operators with periodic coefficients
RF Efendiev - … Matematicheskoi Fiziki, Analiza, Geometrii [Journal of …, 2004 - mathnet.ru
Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical …, 2004•mathnet.ru
The direct and inverse problem of spectral analyses of a class of ordinary differential
equations of order $2 m $ 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 …
equations of order $2 m $ 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 …
Abstract
The direct and inverse problem of spectral analyses of a class of ordinary differential equations of order 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}\} $, , and there exist spectral singularities on the continues spectrum which coincide with the numbers , , The inverse problem of reconstructing of the coefficients by generalized normalizing numbers is solved.
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