We revisit the study of ω-hypercontractions corresponding to a single
weight sequence ω={ωk​}k≥0​ introduced by Olofsson in
\cite{O} and find an analogue of Nagy-Foias characteristic function in this
setting. Explicit construction of characteristic functions is obtained and it
is shown to be a complete unitary invariant. By considering a multi-weight
sequence \clw and \clw-hypercontractions we extend Olofsson's work \cite{O}
in the multi-variable setting. Model for \clw-hypercontractions is obtained
by finding their dilations on certain weighted Bergman spaces over the polydisc
corresponding to the multi-weight sequence \clw. This recovers and provides a
different proof of the earlier work of Curto and Vasilescu \cite{CVPoly, CV}
for γ-contractive multi-operators through a particular choice of
multi-weight sequence.Comment: 31 pages, updated version, comments are welcom