We consider self-adjoint realizations of a second-order elliptic differential expression on with singular interactions of and -type supported on a compact closed smooth hypersurface in . 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 and -interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of do's on closed manifolds and Krein-type resolvent formulae.
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Jussi Behrndt, Gerd Grubb, Matthias Langer, Vladimir Lotoreichik, Spectral asymptotics for resolvent differences of elliptic operators with and -interactions on hypersurfaces. J. Spectr. Theory 5 (2015), no. 4, pp. 697–729