On a comparison between absolute and relative Self-Adjoint Extension Schemes

Abstract

The problem of connecting the operator parameters that label the same self-adjoint extension of a given symmetric operator,  respectively, within the ‘absolute’ von Neumann extension scheme and the ‘relative’ boundary-triplet-induced extension scheme (i.e., a la  Kre˘ın-Viˇsik-Birman) is discussed, and quantitative connections between the two parameters are established in the limit of deficiency  spaces at complex spectral points converging to the deficiency space at a real spectral point.