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 -Δ+P (not necessarily elliptic) in n , n3, 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 {λ j }(Imλ j 0 ) are the scattering poles associated to the operator -Δ+P repeated according to multiplicity, it is proved that for any ε>0 there exists a constant C ε >0 so that #{λ j :|λ j |r, εargλ j π-ε}C ε r n for any r1.

On considère des opérateurs autoadjoints et positifs de la forme -Δ+P (sui ne sont pas nécessairement elliptiques) dans n , n3, 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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