Non-self-adjoint extensions of a Hermitian operator and their characteristic functions (Q1971744)

The authors give a detailed presentation of the theory of extensions of Hermitian operators on Hilbert space whose domains are not necessarily dense and whose spectra have a gap \((\alpha, \beta)\subset \mathbb{R}\). In particular, the characteristic function of an extension is introduced and its boundary values at \(\alpha\) and \(\beta\) are studied.