On the prediction of vector-valued random fields and the spectral distribution of their evanescent component

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Let ( X m , n ) ( m , n ) ∈ Z 2 be a C p -valued wide sense stationary process. We study the prediction theory of such processes according to different total orders on Z 2 . In the case of a “rational order”, we give the spectral distribution of the resulting evanescent component and prove that for two different rational orders, the resulting evanescent components are mutually orthogonal.