Simultaneous Spectral Representations of Isotropically Correlated Random Fields

Abstract

The spectral representations for isotropically correlated two l₁- and l₂-vecotr random fields are given generally in terms of l-vector harmonics and random measures, where l-vector denotes a (2l+l)- dimensional vector in the irreducible representation space of weight l of the rotation group, l＝0 being a scalar and l＝1 an ordinary vector. The representation is derived by making use of the multi-dimensional moving average and the previous work on l-vector functions. The three special cases of interest are discussed in detail ; namely, two scalar random fields, two vector random fields and a scalar and a vector random field.