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

We consider self-adjoint realizations of a second-order elliptic differential expression on R-n with singular interactions of delta and delta'-type supported on a compact closed smooth hypersurface in 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 delta and delta'-interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of psi do's on closed manifolds and Krein-type resolvent formulae.