Improved Berezin-Li-Yau inequalities with a remainder term

2007/11/30 by Timo Weidl, Weidl, Timo · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35P15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P15

paper · pdf · doi:10.48550/arxiv.0711.4925

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

arxiv created 2007/11/30 · openalex publication_date 2007/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an improvement of sharp Berezin type bounds on the Riesz means ∑_k(Λ-λ_k)₊^σ of the eigenvalues λ_k of the Dirichlet Laplacian in a domain if σ≥ 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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• Improved Berezin-Li-Yau inequality and Kröger inequality and consequences

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