J. Behrndt, M. Langer, V. Lotoreichik and J. Rohleder,
Quasi boundary triples and semibounded self-adjoint extensions,
Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), 895–916
Abstract:
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.