## Abstract

This paper is a continuation of our previous investigations on the truncated matrix trigonometric
moment problem in Ukrainian Math. J., 2011, **63**, no. 6, 786-797, and Ukrainian Math. J., 2013, **64**, no. 8, 1199-
1214. In this paper we shall study the truncated matrix trigonometric moment problem with an additional
constraint posed on the matrix measure M_{T}(δ), δ ∈ B(T), generated by the seeked function M(x): M_{T}(∆) =
0, where ∆ is a given open subset of T (called a gap). We present necessary and sufficient conditions for
the solvability of the moment problem with a gap. All solutions of the moment problem with a gap can be
constructed by a Nevanlinna-type formula.

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