# Spectral asymptotics for the semiclassical Dirichlet to Neumann operator

@article{Hassell2015SpectralAF,
title={Spectral asymptotics for the semiclassical Dirichlet to Neumann operator},
author={Andrew Hassell and V. Ivrii},
journal={arXiv: Spectral Theory},
year={2015}
}
• Published 2015
• Mathematics, Physics
• arXiv: Spectral Theory
Let $M$ be a compact Riemannian manifold with smooth boundary, and let $R(\lambda)$ be the Dirichlet-to-Neumann operator at frequency $\lambda$. We obtain a leading asymptotic for the spectral counting function for $\lambda^{-1}R(\lambda)$ in an interval $[a_1, a_2)$ as $\lambda \to \infty$, under the assumption that the measure of periodic billiards on $T^*M$ is zero. The asymptotic takes the form \begin{equation*} N(\lambda; a_1,a_2) = \bigl(\kappa(a_2)-\kappa(a_1)\bigr)\mathsf{vol}'(\partial… Expand
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