Canonical extensions of Hermitian operators

The concept of canonical extensions of Hermitian operators is introduced. Not only are such extensions of interest on their own merits, but they also have significant applications (Theorem 3 in particular) in constructing spaces of boundary values of Hermitian operators with various defect numbers. In recent years boundary-value spaces have found important applications in the study of various classes of extensions of Hermitian operators and in scattering theory. ©2001 Plenum Publishing Corporation.