Improved Berezin-Li-Yau inequalities with a remainder term

Timo Weidl

We give an improvement of sharp Berezin type bounds on the Riesz means ${\sum }_k(\Lambda -{\lambda }_k{)}_{+}^{\sigma }$ of the eigenvalues ${\lambda }_k$ of the Dirichlet Laplacian in a domain if $\sigma \ge 3/2$. It contai…