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New methods in spectral theory of N -body Schrödinger operators

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  • T. Adachi, Kyoto University
  • ,
  • K. Itakura, Ritsumeikan University
  • ,
  • K. Ito, University of Tokyo
  • ,
  • E. Skibsted

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. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-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, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.

TidsskriftReviews in Mathematical Physics
StatusUdgivet - jun. 2021

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