# The truncated matrix trigonometric moment problem with an open gap

Concrete Operators (2015)

- Volume: 2, Issue: 1, page 37-46, electronic only
- ISSN: 2299-3282

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topSergey Zagorodnyuk. "The truncated matrix trigonometric moment problem with an open gap." Concrete Operators 2.1 (2015): 37-46, electronic only. <http://eudml.org/doc/268869>.

@article{SergeyZagorodnyuk2015,

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 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.},

author = {Sergey Zagorodnyuk},

journal = {Concrete Operators},

keywords = {moment problem; generalized resolvent; spectral function; isometric operator; trigonometric moment problem},

language = {eng},

number = {1},

pages = {37-46, electronic only},

title = {The truncated matrix trigonometric moment problem with an open gap},

url = {http://eudml.org/doc/268869},

volume = {2},

year = {2015},

}

TY - JOUR

AU - Sergey Zagorodnyuk

TI - The truncated matrix trigonometric moment problem with an open gap

JO - Concrete Operators

PY - 2015

VL - 2

IS - 1

SP - 37

EP - 46, electronic only

AB - 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.

LA - eng

KW - moment problem; generalized resolvent; spectral function; isometric operator; trigonometric moment problem

UR - http://eudml.org/doc/268869

ER -

## References

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- [2] Berezanskii Ju.M., Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence, RI, 1968 (Russian edition: Naukova Dumka, Kiev, 1965) Zbl0142.37203
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- [7] Inin O.T., A truncated matrix trigonometric moment problem, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 5 (84), 49-57 (in Russian)
- [8] Krein M.G., Nudelman A.A., The Markov moment problem and extremal problems. Ideas and problems of P. L. Cebysev and A. A. Markov and their further development, Translations of Mathematical Monographs. Vol. 50. Providence, R.I., American Mathematical Society (AMS), 1977
- [9] Zagorodnyuk S.M., The truncated matrix trigonometric moment problem: the operator approach, Ukrainian Math. J., 2011, 63, no. 6, 786-797 [WoS]
- [10] Zagorodnyuk S.M., Nevanlinna formula for the truncated matrix trigonometric moment problem, Ukrainian Math. J., 2013, 64, no. 8, 1199-1214 [11] Zagorodnyuk S.M., Generalized resolvents of symmetric and isometric operators: the Shtraus approach, Ann. Funct. Anal., 2013, http://www.emis.de/journals/AFA/ Zbl1273.42002

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