Regular Unitary Dilation of Commuting Contractions and Markovian Representationsof Gaussian Stationary Processes on the Set Z(2)

摘要

The concept of regular unitary dilation of a pair of commuting contractions isshown to be intimately related to Markovian like subspaces with respect to a pair of commuting unitary operators. Starting from this observation, a two dimensional Markovian like representation problem is studied geometrically. By using the geometric properties of the state spaces and some elementary properties of the two variable Hardy spaces, the spectral domain description of regular and coregular representations is given.