## 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

### MSC:

 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

### Keywords:

Riesz mean; Lieb-Thirring conjecture