Spectral estimates for resolvent differences of self-adjoint elliptic operators

Behrndt, Jussi and Langer, Matthias and Lotoreichik, Vladimir (2013) Spectral estimates for resolvent differences of self-adjoint elliptic operators. Integral Equations and Operator Theory, 77 (1). pp. 1-37. ISSN 0378-620X

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    Abstract

    The concept of quasi boundary triples and Weyl functions from extension theory of symmetric operators in Hilbert spaces is developed further and spectral estimates for resolvent differences of two self-adjoint extensions in terms of general operator ideals are proved. The abstract results are applied to self-adjoint realizations of second order elliptic differential operators on bounded and exterior domains, and partial differential operators with δ-potentials supported on hypersurfaces are studied.