Spectral estimates for resolvent differences of self-adjoint elliptic operators

Abstract

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 ${\delta }^{\prime }$-potentials supported on hypersurfaces.

40 pages, submitted

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Cited by in corpus (7)

• On the spectral properties of Dirac operators with electrostatic $\delta$-shell interactions
• Schrödinger operators with δ- and δ'-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
• Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• Quasi boundary triples and semibounded self-adjoint extensions
• Scattering of particles bounded to an infinite planar curve
• Trace formulae for Schrödinger operators with singular interactions