Quasi boundary triples and semi-bounded self-adjoint extensions. Issue 5 (28th June 2017)

• Record Type: Journal Article
• Authors: Behrndt, Jussi; Langer, Matthias; Lotoreichik, Vladimir; Rohleder, Jonathan
• Is Part Of: Proceedings. Volume 147:Issue 5(2017)
• Page Start: 895
• Page End: 916
• Publication Date: 2017-06-28
• Subjects: semi-bounded operator, -- boundary triple, -- Weyl function, -- elliptic differential operator, -- Dirichlet–Neumann map; Primary 35P15, -- 47F05, -- Secondary 35P05, -- 47B25; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210516000421
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : In this note semi-bounded 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 partial differential equations on domains with non-compact boundaries.