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The truncated matrix trigonometric moment problem with an open gap

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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.
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2
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1
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otrzymano
2014-04-25
zaakceptowano
2014-10-17
online
2014-12-12
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Bibliografia
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  • [1] Ando T., Truncated moment problems for operators, Acta Sci. Math. (Szeged), 1970, 31, no. 4, 319-334
  • [2] Berezanskii Ju.M., Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence, RI, 1968 (Russianedition: Naukova Dumka, Kiev, 1965)
  • [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
  • [4] Chumakin M.E., Solutions of the truncated trigonometric moment problem, Uchen. zapiski Ulyanovskogo pedag. instituta,1966, 20, issue 4, 311-355, (in Russian)
  • [5] Fritzsche B., Kirstein B., Thematricial Carathéodory problem in both nondegenerate and degenerate cases, Oper. Theory Adv.Appl., 2006, 165, 251-290
  • [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)
  • [7] Inin O.T., A truncated matrix trigonometric moment problem, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 5 (84), 49-57 (inRussian)
  • [8] Krein M.G., Nudelman A.A., The Markov moment problem and extremal problems. Ideas and problems of P. L. Cebysev andA. A. Markov and their further development, Translations of Mathematical Monographs. Vol. 50. Providence, R.I., AmericanMathematical 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/
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Bibliografia
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bwmeta1.element.doi-10_2478_conop-2014-0003
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