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Concrete Operators

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The truncated matrix trigonometric moment problem with an open gap

Sergey Zagorodnyuk
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  • School of Mathematics and Mechanics, Karazin Kharkiv National University, Svobody Sq., 4, 61022 Kharkiv, Ukraine
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Published Online: 2014-12-12 | DOI: https://doi.org/10.2478/conop-2014-0003

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.

Keywords : moment problem; generalized resolvent; spectral function; isometric operator

References

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  • [1] Ando T., Truncated moment problems for operators, Acta Sci. Math. (Szeged), 1970, 31, no. 4, 319-334 Google Scholar

  • [2] Berezanskii Ju.M., Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence, RI, 1968 (Russian edition: Naukova Dumka, Kiev, 1965) Google Scholar

  • [3] Chen G.-N., Hu Y.-J., On the multiple Nevanlinna-Pick matrix interpolation in the class 'p and the Carathéodory matrix coefficient problem, Linear Algebra Appl., 1998, 283, 179-203 Google Scholar

  • [4] Chumakin M.E., Solutions of the truncated trigonometric moment problem, Uchen. zapiski Ulyanovskogo pedag. instituta, 1966, 20, issue 4, 311-355, (in Russian) Google Scholar

  • [5] Fritzsche B., Kirstein B., Thematricial Carathéodory problem in both nondegenerate and degenerate cases, Oper. Theory Adv. Appl., 2006, 165, 251-290 Google Scholar

  • [6] Ilmushkin G.M., Turitsyn A.B., A truncated operator trigonometric moment problem, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 7, 17-21, (in Russian) Google Scholar

  • [7] Inin O.T., A truncated matrix trigonometric moment problem, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 5 (84), 49-57 (in Russian) Google Scholar

  • [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 Google Scholar

  • [9] Zagorodnyuk S.M., The truncated matrix trigonometric moment problem: the operator approach, Ukrainian Math. J., 2011, 63, no. 6, 786-797 Web of ScienceGoogle Scholar

  • [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/ Google Scholar

About the article

Received: 2014-04-25

Accepted: 2014-10-17

Published Online: 2014-12-12


Citation Information: Concrete Operators, Volume 2, Issue 1, ISSN (Online) 2299-3282, DOI: https://doi.org/10.2478/conop-2014-0003.

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© 2014 Sergey Zagorodnyuk. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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