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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 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.

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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