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On V-Extremal Solutions of the Moment Problem

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Abstract

We study the density problem for a set of polynomials in the space \(L_\sigma ^1 ( - \infty ,\infty )\), where σ is a measure with finite moments. The approach to this problem is based on methods of the theory of moments, which allows one to formulate sufficient conditions in terms of Nevanlinna functions.

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REFERENCES

  1. M. A. Naimark, “Extremal spectral functions of a symmetric operator,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 11 (1947), no. 4, 327-344.

    Google Scholar 

  2. R. Nevanlinna, “Asymptotische Entwicklungen beschränkter Funktionen und das Stieltjessche Momentenproblem,” Ann. Acad. Sci. Fenn. (A), 18 (1922), no. 5, 1-52.

    Google Scholar 

  3. F. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York, 1964.

    Google Scholar 

  4. N. I. Akhiezer, Classical Moment Problem and Some Related Problems of Analysis [in Russian], Fizmatgiz, Moscow, 1961.

    Google Scholar 

  5. I. M. Glazman and P. B. Naiman, “On the convex hull of orthogonal spectral functions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 102 (1955), no. 3, 445-448.

    Google Scholar 

  6. M. Yu. Kuvshinov, “V-extremal solutions of the moment problem,” Uspekhi Mat. Nauk [Russian Math. Surveys], 54 (1999), no. 2, 163-164.

    Google Scholar 

  7. Ch. Berg and J. P. R. Christensen, “Density question in the classical theory of moments,” Ann. Inst. Fourier (Grenoble), 31 (1981), no. 3, 99-114.

    Google Scholar 

  8. H. Hamburger, “Ñber eine Erweiterung des Stieltjesschen Momentenproblems,” Math. Ann., 81 (1920), Math. Ann., 82 (1921).

  9. M. G. Krein, “On the indeterminate case of the Sturm-Liouville boundary-value problem in the interval (0,?),” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 16 (1952), no. 4, 293-324.

    Google Scholar 

  10. B. Ya. Levin, Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow, 1956.

    Google Scholar 

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  1. M. V. Lomonosov Moscow State University, Russia

    M. Yu. Kuvshinov

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  1. M. Yu. Kuvshinov
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Kuvshinov, M.Y. On V-Extremal Solutions of the Moment Problem. Mathematical Notes 72, 362–372 (2002). https://doi.org/10.1023/A:1020551421470

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