Improved Berezin-Li-Yau inequalities with a remainder term

Details Improved Berezin-Li-Yau inequalities with a remainder term Improved Berezin-Li-Yau inequalities with a remainder term

2007-11-30

arxiv.org/abs/0711.4925v1

Mathematics

Spectral Theory

Dedicated to M. Sh. Birman on the occasion of his 80th birthday

Scientific paper

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 $\sigma\geq 3/2$. It contains a correction term of the order of the standard second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains.

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