Minimax interpolation of harmonizable sequences

The problem of estimation of the functional $A_N \xi =\sum _{j = 0}^{N} a_j \xi _j$ that depends on unknown values $\xi _j$, $j=0,1,\dots ,N$, of a harmonizable symmetric $\alpha$-stable random sequence $\xi _n$, $n\in \mathbb Z$, by using observations of the sequence at the points $n\in \mathbb Z\setminus \{0,1,\dots ,N\}$ is studied under one of the conditions, either a condition of spectral certainty or a condition of spectral uncertainty. Expressions for calculating the value of the error and spectral characteristic of the optimal linear estimator of the functional are obtained under the condition of spectral certainty in the case where the spectral density of a sequence is known. In the case of spectral uncertainty where the spectral density of a sequence is not known but a class of admissible spectral densities is given, we propose relations to determine the least favorable spectral density and the minimax spectral characteristic.