Quasi boundary triples and semibounded self-adjoint extensions

Behrndt, Jussi and Langer, Matthias and Lotoreichik, Vladimir and Rohleder, Jonathan (2017) Quasi boundary triples and semibounded self-adjoint extensions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 147 (5). pp. 895-916. ISSN 0308-2105 (https://doi.org/10.1017/S0308210516000421)

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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.