Spectral estimates for resolvent differences of self-adjoint elliptic operators

Details Spectral estimates for resolvent differences of self-adjoint elliptic operators Spectral estimates for resolvent differences of self-adjoint elliptic operators

2010-12-21

arxiv.org/abs/1012.4596v1

Mathematics

Spectral Theory

40 pages, submitted

Scientific paper

The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed, and general theorems on resolvent differences belonging to operator ideals are proved. The results are applied to second order elliptic differential operators on bounded and exterior domains, and to partial differential operators with $\delta$ and $\delta'$-potentials supported on hypersurfaces.

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