Spectral asymptotics for resolvent differences of elliptic operators with δ and δ'-interactions on hypersurfaces

Jussi Behrndt, Gerd Grubb, Matthias Langer, Vladimir Lotoreichik

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We consider self-adjoint realizations of a second-order elliptic differential expression on Rn with singular interactions of δ and δ'-type supported on a compact closed smooth hypersurface in Rn. 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 and δ'-interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of ψdo's on closed manifolds and Krein-type resolvent formulae.
Original languageEnglish
Pages (from-to)697-729
Number of pages33
JournalJournal of Spectral Theory
Issue number4
Publication statusPublished - 1 Dec 2015


  • Krein-type resolvent formulae
  • pseudodifferential methods
  • spectral asymptotics

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