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 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.