Canonical operator models over reinhardt domains

Through the works of many, now it is well known that the existence of dilation to the direct sum of a weighted shift is guaranteed by a positivity condition and a convergence condition. But the uniqueness of dilation is still not well understood. In this paper we show that a theory of canonical operator models, not just the existence of dilation, can be achieved for general weighted shifts, with a level of sophistication at least close to that for the d-shifts on the symmetric Fock spaces. Most techniques used in the paper are known, but we do have new ingredients which give a clearer picture even on the symmetric Fock space, where a nice theory has been developed by Arveson.