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

Behrndt, Jussi and Grubb, Gerd and Langer, Matthias and Lotoreichik, Vladimir (2015) Spectral asymptotics for resolvent differences of elliptic operators with δ and δ'-interactions on hypersurfaces. Journal of Spectral Theory, 5 (4). pp. 697-729. ISSN 1664-0403

[thumbnail of Behrndt-etal-JST2015-spectral-asymptotics-for-resolvent-differences-of-elliptic-operators]
Preview
Text (Behrndt-etal-JST2015-spectral-asymptotics-for-resolvent-differences-of-elliptic-operators)
Behrndt_etal_JST2015_spectral_asymptotics_for_resolvent_differences_of_elliptic_operators.pdf
Accepted Author Manuscript

Download (454kB)| Preview

    Abstract

    We consider self-adjoint realizations of a second-order elliptic differential expression on R n with singular interactions of δ and δ'-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 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.

    ORCID iDs

    Behrndt, Jussi, Grubb, Gerd, Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914 and Lotoreichik, Vladimir;