On the distribution of resonances for some asymptotically hyperbolic manifolds

R. G. Froese; Peter D. Hislop

Journées équations aux dérivées partielles (2000)

  • page 1-16
  • ISSN: 0752-0360

Abstract

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We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute S -matrix that is unitary for real values of the energy. This paramatrix is the S -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance counting function requires estimates on the growth of the relative scattering phase, and singular values of a family of integral operators.

How to cite

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Froese, R. G., and Hislop, Peter D.. "On the distribution of resonances for some asymptotically hyperbolic manifolds." Journées équations aux dérivées partielles (2000): 1-16. <http://eudml.org/doc/93404>.

@article{Froese2000,
abstract = {We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute $S$-matrix that is unitary for real values of the energy. This paramatrix is the $S$-matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance counting function requires estimates on the growth of the relative scattering phase, and singular values of a family of integral operators.},
author = {Froese, R. G., Hislop, Peter D.},
journal = {Journées équations aux dérivées partielles},
keywords = {resonance counting function; asymptotically hyperbolic manifolds},
language = {eng},
pages = {1-16},
publisher = {Université de Nantes},
title = {On the distribution of resonances for some asymptotically hyperbolic manifolds},
url = {http://eudml.org/doc/93404},
year = {2000},
}

TY - JOUR
AU - Froese, R. G.
AU - Hislop, Peter D.
TI - On the distribution of resonances for some asymptotically hyperbolic manifolds
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 16
AB - We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute $S$-matrix that is unitary for real values of the energy. This paramatrix is the $S$-matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance counting function requires estimates on the growth of the relative scattering phase, and singular values of a family of integral operators.
LA - eng
KW - resonance counting function; asymptotically hyperbolic manifolds
UR - http://eudml.org/doc/93404
ER -

References

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