On the distribution of resonances for some asymptotically hyperbolic manifolds
Journées équations aux dérivées partielles (2000), article no. 7, 16 p.

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.

@article{JEDP_2000____A7_0,
     author = {Froese, R. G. and Hislop, Peter D.},
     title = {On the distribution of resonances for some asymptotically hyperbolic manifolds},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Universit\'e de Nantes},
     year = {2000},
     zbl = {01808697},
     mrnumber = {2001j:58054},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2000____A7_0}
}
Froese, R. G.; Hislop, Peter D. On the distribution of resonances for some asymptotically hyperbolic manifolds. Journées équations aux dérivées partielles (2000), article  no. 7, 16 p. http://www.numdam.org/item/JEDP_2000____A7_0/

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