Improved Berezin-Li-Yau inequalities with a remainder term

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We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(Λ-λ_k)_+^σ$ of the eigenvalues $λ_k$ of the Dirichlet Laplacian in a domain if $σ\geq 3/2$. 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.
Dedicated to M. Sh. Birman on the occasion of his 80th birthday

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Spectral Theory, Mathematical Physics, 35P15

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http://salesiana.dossiersoluciones.com/handle/123456789/143246

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.4925
 http://arxiv.org/abs/0711.4925

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arXiv