Spectral asymptotics for the semiclassical Dirichlet to Neumann operator

  • Andrew Hassell

    Australian National University, Canberra, Australia
  • Victor Ivrii

    University of Toronto, Canada

Abstract

Let be a compact Riemannian manifold with smooth boundary, and let be the Dirichlet–to–Neumann operator at frequency . The semiclassical Dirichlet–to–Neumann operator is defined to be . We obtain a leading asymptotic for the spectral counting function for in an interval as , under the assumption that the measure of periodic billiards on is zero. The asymptotic takes the form

where is given explicitly by

Cite this article

Andrew Hassell, Victor Ivrii, Spectral asymptotics for the semiclassical Dirichlet to Neumann operator. J. Spectr. Theory 7 (2017), no. 3, pp. 881–905

DOI 10.4171/JST/180