Spectral asymptotics for resolvent differences of elliptic operators with $\delta$ and $\delta^\prime$interactions on hypersurfaces
Abstract
We consider selfadjoint realizations of a secondorder elliptic differential expression on ${\mathbb R}^n$ with singular interactions of $\delta$ and $\delta^\prime$type supported on a compact closed smooth hypersurface in ${\mathbb R}^n$. In our main results we prove spectral asymptotics formulae with refined remainder estimates for the singular values of the resolvent difference between the standard selfadjoint realizations and the operators with a $\delta$ and $\delta^\prime$interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of $\psi$do's on closed manifolds and Kreintype resolvent formulae.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 arXiv:
 arXiv:1404.2791
 Bibcode:
 2014arXiv1404.2791B
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 to appear in J. Spectr. Theory