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 Kreĭn-Višik-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.

Mathematics Subject Classification (2020):

• 47B25
• 47B93

Key words:

• Self-adjoint operators on Hilbert space
• self-adjoint extensions
• von Neumann's extension theory
• Kreĭn-Višik-Birman extension theory
• extension parameters
• boundary triplets