On the prediction theory of two-parameter stationary random fields

The paper develops the spectral theory corresponding to the various time domain Wold decompositions of a discrete two-parameter stationary second-order random field (ssorf). Appropriate Szegö-type error formulas are established. Minimality and interpolability are defined for ssorf's and sufficient spectral criteria for these are derived. Partial results are also obtained which help to determine, via spectral methods, some of the multiplicities introduced by Kallianpur and Mandrekar in their time domain analysis of ssorf's.