Linear interpolation problem for random fields on Abelian compact groups (Q2737212)

The problem of estimation of the functional NEWLINE\[NEWLINEA_N\xi=\sum_{j=0}^N\int_{G}a(g,j)\xi(g,j)dgNEWLINE\]NEWLINE of the unknown values of a homogeneous random field \(\xi(g,j)\) from observations of the field \(\xi(g,j)+\eta(g,j)\) at points from the set NEWLINE\[NEWLINEG\times Z^{N+}=\{(g,j) : g\in G, j\in Z\backslash\{0,1,\dots,N\}\}NEWLINE\]NEWLINE is considered. Here \(\eta(g,j)\) is an uncorrelated with \(\xi(g,j)\) homogeneous random field. The mean square error and the minimax spectral characteristics of the optimal linear estimator of the functional \(A_N\xi\) are obtained provided that the spectral densities of the fields are unknown, but the class \(D\) of possible densities is given.