Spectral asymptotics for manifolds with cylindrical ends

Tanya Christiansen; Maciej Zworski

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 1, page 251-263
  • ISSN: 0373-0956

Abstract

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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 , 𝒪 ( r n ) , where n is the dimension of the manifold.

How to cite

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Christiansen, Tanya, and Zworski, Maciej. "Spectral asymptotics for manifolds with cylindrical ends." Annales de l'institut Fourier 45.1 (1995): 251-263. <http://eudml.org/doc/75116>.

@article{Christiansen1995,
abstract = {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 $r^2,~\{\cal O\} (r^n)$, where $n$ is the dimension of the manifold.},
author = {Christiansen, Tanya, Zworski, Maciej},
journal = {Annales de l'institut Fourier},
keywords = {spectral asymptotics},
language = {eng},
number = {1},
pages = {251-263},
publisher = {Association des Annales de l'Institut Fourier},
title = {Spectral asymptotics for manifolds with cylindrical ends},
url = {http://eudml.org/doc/75116},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Christiansen, Tanya
AU - Zworski, Maciej
TI - Spectral asymptotics for manifolds with cylindrical ends
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 1
SP - 251
EP - 263
AB - 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 $r^2,~{\cal O} (r^n)$, where $n$ is the dimension of the manifold.
LA - eng
KW - spectral asymptotics
UR - http://eudml.org/doc/75116
ER -

References

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  12. [12] S. PATTERSON, The Selberg zeta function of a Kleinian group, in "Number theory, trace formulas and discrete group", p. 409-441, Academic Press, Boston, 1989. Zbl0668.10036MR91c:11029
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