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Resonance expansions of scattered waves. (English) Zbl 1032.35148
From the introduction: The purpose of this paper is to describe expansions of solutions to the wave equation on \(\mathbb{R}^n\) with a compactly supported perturbation present. We show that under a separation condition on resonances, the solutions can be expanded in terms of resonances close to the real axis, modulo an error rapidly decaying in time. To avoid the discussion of particular aspects of potential gravitational, or obstacle scattering, the results are stated using the abstract “black box” formalism of J. Sjöstrand and the second author [J. Amer. Math. Soc. 4, 729-769 (1991; Zbl 0752.35046)].

MSC:
35P25 Scattering theory for PDEs
35L05 Wave equation
81U20 \(S\)-matrix theory, etc. in quantum theory
47F05 General theory of partial differential operators
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