Trace identities of the type derived by Harrell-Stubbe, and later generalized by Levitin-Parnovski, proved to be a very efficient procedure to produce universal Yang-type bounds for eigenvalues of the Dirichlet Laplacian.

In this talk we show how these identities can be used to produce new universal Weyl-type bounds for averages of eigenvalues, and provide alternative routes to the Berezin-Li-Yau inequality as viewed by Laptev and Weidl.

This is joint work with Professor Evans Harrell of Georgia Tech.

A preprint is available at lanl.arxiv.org/abs/0705.3673