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 , où 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 , where 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},
mrnumber = {96d:35100},
zbl = {0818.58046},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1455/}
}
TY - JOUR AU - Christiansen, Tanya AU - Zworski, Maciej TI - Spectral asymptotics for manifolds with cylindrical ends JO - Annales de l'Institut Fourier PY - 1995 SP - 251 EP - 263 VL - 45 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1455/ DO - 10.5802/aif.1455 LA - en ID - AIF_1995__45_1_251_0 ER -
%0 Journal Article %A Christiansen, Tanya %A Zworski, Maciej %T Spectral asymptotics for manifolds with cylindrical ends %J Annales de l'Institut Fourier %D 1995 %P 251-263 %V 45 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1455/ %R 10.5802/aif.1455 %G en %F AIF_1995__45_1_251_0
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://www.numdam.org/articles/10.5802/aif.1455/
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