Riesz means of bound states and semiclassical limit connected with a Lieb-Thirring’s conjecture. (English) Zbl 0717.35062

The authors study the Riesz mean of order \(\gamma\) of h-admissible operators. They show that it admits an asymptotic expansion in powers of h, up to order \([\gamma]+1\) (or \(\gamma\) if \(\gamma\) is integer).
The coefficients of this expansion are explicitly computed, and a link is made with a Lieb-Thirring conjecture in the case of the Schrödinger operator.
Reviewer: A.Martinez


35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory