Poisson formulae for resonances. (English) Zbl 1255.35084
Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau 1996-1997, Exp. No. XIII, 14 p. (1997).
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.
MSC:
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 |