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\(N\)-body resolvent estimates. (English) Zbl 0851.35101

The paper is devoted to microlocal resolvent estimates for a large class of \(N\)-body Schrödinger operators. The authors attempt to generalize known microlocal resolvent estimates as far as possible by a new method that appears to be elementary and easy to handle. The potential is considered to have two parts – a smooth one and a compactly supported one. The authors prove estimates involving only pseudo-differential localization for the intercluster motion when localizing to some geometrically determined regions of the configuration space. First, they develop a calculus that consecutively is used for proving resolvent estimates. Next, the concomitant statements are converted into more natural geometrical ones. This means estimates that (converted to time decay estimates) reflect the expectation for desintegration of the motion into stable clusters moving freely in the remote future. The paper is mostly selfcontained, but for the Mourre estimate.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
81U10 \(n\)-body potential quantum scattering theory
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