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.
- Krein-type resolvent formulae
- pseudodifferential methods
- spectral asymptotics
Behrndt, J., Grubb, G., Langer, M., & Lotoreichik, V. (2015). Spectral asymptotics for resolvent differences of elliptic operators with δ and δ'-interactions on hypersurfaces. Journal of Spectral Theory, 5(4), 697-729. https://doi.org/10.4171/JST/111