The spectral measure of a regular stationary random field with the weak or strong commutation property (Q688037)

The problem of the spectral measure of a regular stationary random field with the weak or strong commutation property is studied. It is shown that a regular stationary random field over the plane possesses the weak commutation property if and only if its spectral density function admits a weakly outer factorization in the Hardy space \(H^ 2\) on the 2- dimensional torus. A similar statement is proved for the strong commutation property. Application to prediction is discussed.