2014/03/21 by Sergey M. Zagorodnyuk, Zagorodnyuk, Sergey M.
Mathematics · #44A60 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:44A60
paper · pdf · doi:10.48550/arxiv.1403.5592
14 pages. arXiv admin note: text overlap with arXiv:1401.5413
arxiv created 2015/05/16 · arxiv updated 2015/05/19
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_\mathbbT(δ), δ∈ \mathfrakB(\mathbbT), generated by the seeked function M(x): M_\mathbbT(Δ) = 0, where Δ is a given open subset of \mathbbT (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.