Commutator algebra and resolvent estimates. (English) Zbl 0814.35086

Gérard, Christian; Isozaki, Hiroshi; Skibsted, Erik

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].

Reviewer: A.Martinez (Villetaneuse)

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