Canonical operator models over Reinhardt domains (Q2470791)

The starting point of the paper is a result in the Sz.-Nagy--Foiaş theory, asserting that a Hilbert space operator can be dilated to a vector-valued Hardy space (i.e., it is unitarily equivalent to the compression to a coinvariant subspace of the multiplication operator with the independent variable on the corresponding vector-valued Hardy space) if and only if it is purely contractive. The author is interested to replace in this statement the multiplication operator by a weighted shift (as many of the cited authors already did), exhibiting a comprehensive theory of canonical models over Reinhardt domains. Although most of the techniques are known, the author uses some new ingredients, offering supplementary details even on symmetric Fock spaces, a case previously studied by W.\,Arveson.