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Poisson formulae for resonances. (English) Zbl 1255.35084
From the text: The purpose of this exposé is to present a new proof of the Poisson formula for resonances. It comes essentially from joint work with {\it L. Guillopé} [J. Funct. Anal. 129, No. 2, 364--389 (1995; Zbl 0841.58063)] and the main point is that we avoid the use of Lax-Phillipos theory and in particular of the strong Huyghens principle. That was necessary for extending the formula to the case of surfaces with infinite volume hyperbolic ends. It was however the Lax-Phillips theory which provided the original motivation for the formula.

35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35P25Scattering theory (PDE)
47A40Scattering theory of linear operators
47F05Partial differential operators
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