Spectral asymptotics for the semiclassical Dirichlet to Neumann operator
Spectral asymptotics for the semiclassical Dirichlet to Neumann operator
Let M be a compact Riemannian manifold with smooth boundary, and let R(\lambda) be the Dirichlet–to–Neumann operator at frequency \lambda . The semiclassical Dirichlet–to–Neumann operator R_{\mathrm {scl}}(\lambda) is defined to be \lambda^{-1} R(\lambda) . We obtain a leading asymptotic for the spectral counting function for R_{\mathrm {scl}}(\lambda) in an interval …