Quasi boundary triples and semibounded self-adjoint extensions

TL;DR

This paper explores how quasi boundary triples can be used to analyze semibounded self-adjoint extensions of symmetric operators, providing new conditions for self-adjoint realizations and linking Weyl function decay to spectral bounds.

Contribution

It introduces new sufficient conditions for self-adjoint extensions using quasi boundary triples and relates Weyl function decay to spectral estimates, with applications to elliptic PDEs.

Findings

New criteria for self-adjoint extensions

Decay of Weyl functions linked to spectral bounds

Applications to elliptic PDEs on non-compact domains

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.