Interpolation of multidimensional stationary sequences

The problem of optimal estimation is considered for the linear functional $A_{N}\vec{\xi}=\sum_{j=0}^{N}\vec{a}(j)\vec {\xi }(j)$, where $\{\vec{\xi}(j)\}$ and $\{\vec{\eta}(j)\}$ are multidimensional stationary stochastic sequences. The estimation is based on observations of the sequence $\vec {\xi} (j)+\vec {\eta} (j)$ for $j \in Z\setminus {\left\{ {0,\dots, N} \right\}}$. We obtain formulas for calculating the mean-square error and spectral characteristic of the optimal estimate of the functional. The least favorable spectral densities and minimax spectral characteristics of the optimal estimates of the functional are found for some classes of spectral densities.