Spectral estimates for resolvent differences of self-adjoint elliptic operators

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik

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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.
Original languageEnglish
Pages (from-to)1-37
Number of pages37
JournalIntegral Equations and Operator Theory
Volume77
Issue number1
Early online date1 Jul 2013
DOIs
Publication statusPublished - Sep 2013

Keywords

  • elliptic operator
  • self-adjoint extension
  • operator ideal
  • delta-potential
  • quasi boundary triple
  • Weyl function

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