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Zeroth order conjugate operator in $N$-body Schrödinger operators

Kenichi Ito (University of Tokyo)
Math/Phys Seminar
Thursday, 4 October, 2018, at 14:15-15:00, in Aud. D2 (1531-119)

We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. The main results are Rellich's theorem and the limiting absorption principle. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for $L^2$-eigenfunctions. Each pair-potential is a sum of a long-range term with first order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type. The setup can also include hard-core interactions. Our proof consists of a systematic use of commutators with a 'zeroth order' operator, not like the standard 'first order' conjugate operator in the Mourre theory. In particular, our proofs do not rely on Mourre's differential inequality technique.

This talk is based on a recent joint work with T. Adachi, K. Itakura and E. Skibsted.

Contact person: Erik Skibsted