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Semiclassical resolvent estimates for $$N$$-body Schrödinger operators. (English) Zbl 0739.35047
(Author’s summary:) We prove for a generalized $$N$$-body Schrödinger operator that the non-trapping condition on the classical Hamiltonian and all classical sub-Hamiltonians is both necessary and sufficient for obtaining good semiclassical bounds on the boundary values of the resolvent and their energy derivatives. We accomplish this by generalizing Gérard’s geometrical construction of an escape function for three-body problems to $$N$$-body problems.

MSC:
 35P05 General topics in linear spectral theory for PDEs 35J10 Schrödinger operator, Schrödinger equation 70F10 $$n$$-body problems
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References:
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