Quasi boundary triples and semibounded self-adjoint extensions

Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik, Jonathan Rohleder

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In this note semibounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on the parameters in the boundary space to induce self-adjoint realizations, and to relate the decay of the Weyl function to estimates on the lower bound of the spectrum. The abstract results are illustrated with uniformly elliptic second-order PDEs on domains with non-compact boundaries.
Original languageEnglish
Pages (from-to)895-916
Number of pages22
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number5
Early online date28 Jun 2017
Publication statusPublished - 6 Oct 2017


  • semi-bounded self-adjoint
  • symmetric operators
  • quasi boundary triples
  • Weyl functions


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