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We derive sharp approximation error bounds for inverse block Toeplitzmatrices associated with multivariate long-memory stationary processes. Theerror bounds are evaluated for both column and row sums. These results are usedto prove the strong convergence of the solutions of general block Toeplitzsystems. A crucial part of the proof is to bound sums consisting of the Fouriercoefficients of the phase function attached to the singular symbol of theToeplitz matrices.

Approximations of inverse block Toeplitz matrices and Baxter-type theorems for long-memory processes