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 MT(δ), δ ∈ B(T), generated by the seeked function M(x): MT(∆) = 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.
@article{bwmeta1.element.doi-10_2478_conop-2014-0003,
author = {Sergey Zagorodnyuk},
title = {The truncated matrix trigonometric moment problem with an open gap},
journal = {Concrete Operators},
volume = {2},
year = {2015},
zbl = {06477133},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_conop-2014-0003}
}
Sergey Zagorodnyuk. The truncated matrix trigonometric moment problem with an open gap. Concrete Operators, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_conop-2014-0003/
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