# The Detectable Subspace for the Friedrichs Model

Brown, B.M., Marletta, Marco, Naboko, Sergey, Wood, Ian (2019) The Detectable Subspace for the Friedrichs Model. Integral Equations and Operator Theory, . ISSN 0378-620X. E-ISSN 1420-8989. (doi:10.1007/s00020-019-2548-9)

PDF - Publisher pdf

 Preview
PDF - Author's Accepted Manuscript
Restricted to Repository staff only
This paper discusses how much information on a Friedrichs model operator can be detected from measurements on the boundary'. We use the framework of boundary triples to introduce the generalised Titchmarsh-Weyl M-function and the detectable subspaces which are associated with the part of the operator which is accessible from boundary measurements'. The Friedrichs model, a finite rank perturbation of the operator of multiplication by the independent variable, is a toy model that is used frequently in the study of perturbation problems. We view the Friedrichs model as a key example for the development of the theory of detectable subspaces, because it is sufciently simple to allow a precise description of the structure of the detectable subspace in many cases, while still exhibiting a variety of behaviours. The results also demonstrate an interesting interplay between modern complex analysis, such as the theory of Hankel operators, and operator theory