On the distribution of scattering poles for perturbations of the Laplacian
Annales de l'Institut Fourier, Volume 42 (1992) no. 3, p. 625-635

We consider selfadjoint positively definite operators of the form $-\Delta +P$ (not necessarily elliptic) in ${ℝ}^{n}$, $n\ge 3$, odd, where $P$ is a second-order differential operator with coefficients of compact supports. We show that the number of the scattering poles outside a conic neighbourhood of the real axis admits the same estimates as in the elliptic case. More precisely, if $\left\{{\lambda }_{j}\right\}\left(Im{\lambda }_{j}\ge {0}_{\right)}$ are the scattering poles associated to the operator $-\Delta +P$ repeated according to multiplicity, it is proved that for any $\epsilon >0$ there exists a constant ${C}_{\epsilon }>0$ so that $#\left\{{\lambda }_{j}:|{\lambda }_{j}|\le r$, $\epsilon \le arg{\lambda }_{j}\le \pi -\epsilon \right\}\le {C}_{\epsilon }{r}^{n}$ for any $r\ge 1$.

On considère des opérateurs autoadjoints et positifs de la forme $-\Delta +P$ (sui ne sont pas nécessairement elliptiques) dans ${ℝ}^{n}$, $n\ge 3$, où $P$ est un opérateur différentiel du deuxième ordre, à coefficients à support compact. On montre que le nombre des pôles de la diffusion en dehors d’un voisinage conique de l’axe réel admet des estimations semblables au cas elliptique.

@article{AIF_1992__42_3_625_0,
author = {Vodev, Georgi},
title = {On the distribution of scattering poles for perturbations of the Laplacian},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
address = {28 - Luisant},
volume = {42},
number = {3},
year = {1992},
pages = {625-635},
doi = {10.5802/aif.1303},
zbl = {0738.35054},
mrnumber = {93i:35098},
language = {en},
url = {http://www.numdam.org/item/AIF_1992__42_3_625_0}
}

Vodev, Georgi. On the distribution of scattering poles for perturbations of the Laplacian. Annales de l'Institut Fourier, Volume 42 (1992) no. 3, pp. 625-635. doi : 10.5802/aif.1303. http://www.numdam.org/item/AIF_1992__42_3_625_0/

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