Quasi boundary triples and semibounded self-adjoint extensions

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.

to appear in Proc. Roy. Soc. Edinburgh Sect. A

References in corpus (3)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

Cited by in corpus (7)

• Asymptotics of the bound state induced by $\delta$-interaction supported on a weakly deformed plane
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• Quantum cavities with alternating boundary conditions
• The strong Legendre condition and the well-posedness of mixed Robin problems on manifolds with bounded geometry
• Boundary triples for a family of degenerate elliptic operators of Keldysh type
• Canonical decomposition of dissipative linear relations
• Perspectives on General Left-Definite Theory