Spectral asymptotics for manifolds with cylindrical ends
Annales de l'Institut Fourier, Tome 45 (1995) no. 1, pp. 251-263.

Le spectre du laplacien sur les variétés à bouts cyclindriques est composé d’un spectre continu à multiplicité localement finie et de valeurs propres plongées. Nous démontrons une formule asymptotique du type Weyl pour la somme du nombre de valeurs propres plongées et de la phase de diffusion. En particulier, nous obtenons la limite supérieure optimale du nombre de valeurs propres plongées inférieures ou égales à ${r}^{2},\phantom{\rule{3.33333pt}{0ex}}𝒪\left({r}^{n}\right)$, où $r$ est la dimension de la variété.

The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to ${r}^{2},\phantom{\rule{3.33333pt}{0ex}}𝒪\left({r}^{n}\right)$, where $n$ is the dimension of the manifold.

@article{AIF_1995__45_1_251_0,
author = {Christiansen, Tanya and Zworski, Maciej},
title = {Spectral asymptotics for manifolds with cylindrical ends},
journal = {Annales de l'Institut Fourier},
pages = {251--263},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {45},
number = {1},
year = {1995},
doi = {10.5802/aif.1455},
zbl = {0818.58046},
mrnumber = {96d:35100},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.1455/}
}
Christiansen, Tanya; Zworski, Maciej. Spectral asymptotics for manifolds with cylindrical ends. Annales de l'Institut Fourier, Tome 45 (1995) no. 1, pp. 251-263. doi : 10.5802/aif.1455. http://archive.numdam.org/articles/10.5802/aif.1455/

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