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Structure of the resolvent for three-body potentials. (English) Zbl 0891.35111
The author investigates the three-body scattering matrix of Schrödinger operators. His main result is a proof of Melrose’s conjecture on the three-cluster to three-cluster part of the scattering matrix, stating that it can be written as a sum of Fourier integral operators associated to a certain “broken” geodesic flow. The structure of the paper is as follows: analysis of the two-body resolvent, construction of the approximate eigenfunctions of the Schrödinger operator, construction of the three-body resolvent, facts on the Poisson operator, analysis of the scattering matrix, and finally, asymptotic behavior of the resolvent.

MSC:
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81U10 \(n\)-body potential quantum scattering theory
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