On factoring the polyvariance operator

The minimum phase factorization of bounded Hermitian operators (covariance operators) is an essential ingredient in linear filtering and stochastic control. In a recent article the author studied an analogous class of polynomic filtering and stochastic control problems. The present study uses the concept of a Hilbert scale to establish a minimum phase factorization procedure for the polynomic setting. The linear theory is carried over in its entirety.Supported in part by the US Air Force Office of Scientific Research under Grant No. 78-3500 and the National Science Foundation under Grant 78/8871.