Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain

• Main Authors: Frank, Rupert L., Geisinger, Leander
• Format: Text
• Language: unknown
• Published: arXiv 2011
• Subjects: Spectral Theory math.SP; Mathematical Physics math-ph; FOS Mathematics; FOS Physical sciences; Ari; Laplace; laptev
• Online Access: https://dx.doi.org/10.48550/arxiv.1105.5182; https://arxiv.org/abs/1105.5182

Let -Δdenote the Dirichlet Laplace operator on a bounded open set in \mathbb{R}^d. We study the sum of the negative eigenvalues of the operator -h^2 Δ- 1 in the semiclassical limit h \to 0+. We give a new proof that yields not only the first term of the asymptotic formula but also the second term in...