论文标题
$ \ clw $ -ypertractions及其模型
$\clw$-hypercontractions and their model
论文作者
论文摘要
我们重新访问对对应于单个权重序列$ω= \ {ω_k\} _ {k \ geq0} $的$ω$ -ypertractions的研究。获得了特征函数的明确构造，并显示为完全统一的不变。通过考虑多重量序列$ \ clw $和$ \ clw $ -ypernartions，我们在多变量设置中扩展了Olofsson的工作\ cite {o}。 $ \ clw $ -ypertractions的模型是通过在对应于多重量序列$ \ clw $的polydisc上的某些加权伯格曼空间上的扩张来获得的。这可以通过特定的多重量序列选择$γ$ - 扣除多重序列，以恢复并提供了库尔托和vasilescu \ cite {cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly，cvpoly {cvpoly {cvpoly，通过特定选择的多重量序列的早期工作，提供了不同的证据。
We revisit the study of $ω$-hypercontractions corresponding to a single weight sequence $ω=\{ω_k\}_{k\geq0}$ 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.
