## Commutator algebra and resolvent estimates.(English)Zbl 0814.35086

Yajima, K. (ed.), Spectral scattering theory and applications. Proceedings of a conference on spectral and scattering theory held at Tokyo Institute of Technology, Japan, June 30-July 3, 1992 in honour of Shige Toshi Kuroda on the occasion of his 60th birthday. Tokyo: Kinokuniya Company Ltd.. Adv. Stud. Pure Math. 23, 69-82 (1994).
The authors give a microlocal resolvent estimate for general quantum $$N$$- body problems. This estimate consists in multiplying to the left the out- going boundary value of the resolvent, by a pseudodifferential operator whose symbol is supported in an incoming region of the phase space. Then the resulting operator appears to be bounded on some weighted $$L^ 2$$- spaces. The proof relies on Mourre’s commutator estimates.
For the entire collection see [Zbl 0791.00025].

### MSC:

 35P25 Scattering theory for PDEs 35S05 Pseudodifferential operators as generalizations of partial differential operators 81U10 $$n$$-body potential quantum scattering theory 35J10 Schrödinger operator, Schrödinger equation

### Keywords:

Schrödinger operator; $$N$$-body problem; Mourre estimate