REGULAR UNITARY DILATION OF COMMUTING CONTRACTIONS AND MARKOVIAN REPRESENTATION OF GAUSSIAN STATIONARY-PROCESSES ON Z2

In this paper, we show that the concept of regular unitary dilation of a pair of commuting contractions is intimately related to Markovian-l ike subspaces with respect to a pair of commuting unitary operators. S tarting from this observation, a two-dimensional Markovian-like repres entation problem previously introduced by Attasi is studied geometrica lly. By using the geometric properties of the state spaces and some el ementary properties of two-variable Hardy spaces, the spectral domain description of regular and coregular minimal representations are given .