JournalsjstVol. 5, No. 4pp. 697–729

Spectral asymptotics for resolvent differences of elliptic operators with δ\delta and δ\delta^{\prime}-interactions on hypersurfaces

  • Jussi Behrndt

    TU Graz, Austria
  • Gerd Grubb

    Copenhagen University, Denmark
  • Matthias Langer

    University of Strathclyde, Glasgow, UK
  • Vladimir Lotoreichik

    Nuclear Physics Institute, Řež - Prague, Czech Republic
Spectral asymptotics for resolvent differences of elliptic operators with $\delta$ and $\delta^{\prime}$-interactions on hypersurfaces cover

Abstract

We consider self-adjoint realizations of a second-order elliptic differential expression on Rn\mathbb R^n with singular interactions of δ\delta and δ\delta^\prime-type supported on a compact closed smooth hypersurface in Rn\mathbb R^n. In our main results we prove spectral asymptotics formulae with refined remainder estimates for the singular values of the resolvent difference between the standard self-adjoint realizations and the operators with a δ\delta and δ\delta^\prime-interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of ψ\psido's on closed manifolds and Krein-type resolvent formulae.

Cite this article

Jussi Behrndt, Gerd Grubb, Matthias Langer, Vladimir Lotoreichik, Spectral asymptotics for resolvent differences of elliptic operators with δ\delta and δ\delta^{\prime}-interactions on hypersurfaces. J. Spectr. Theory 5 (2015), no. 4, pp. 697–729

DOI 10.4171/JST/111