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On the strong matrix Hamburger moment problem

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Ukrainian Mathematical Journal Aims and scope

We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized resolvents of symmetric operators.

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References

  1. W. B. Jones, O. Njåstad, and W. J. Thron, “Continued fractions and strong Hamburger moment problems,” Proc. London Math. Soc., (3) 47, No. 2, 363–384 (1983).

  2. W. B. Jones, W. J. Thron, and O. Njåstad, “Orthogonal Laurent polynomials and the strong Hamburger moment problem,” J. Math. Anal. Appl., 98, No. 2, 528–554 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  3. O. Njåstad, “Solutions of the strong Hamburger moment problem,” J. Math. Anal. Appl., 197, 227–248 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  4. W. B. Jones and O. Njåstad, “Orthogonal Laurent polynomials and strong moment theory: a survey,” J. Comput. Appl. Math., 105, No. 1–2, 51–91 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  5. K. K. Simonov, “Strong matrix moment problem of Hamburger,” Meth. Funct. Anal. Top., 12, No. 2, 183–196 (2006).

    MATH  MathSciNet  Google Scholar 

  6. S. M. Zagorodnyuk, “Positive-definite kernels satisfying difference equations,” Meth. Funct. Anal. Top., 16, No. 1, 83–100 (2010).

    MathSciNet  Google Scholar 

  7. A. V. Shtraus, “Generalized resolvents of symmetric operators,” Izv. Akad. Nauk SSSR, 18, 51–86 (1954).

    MATH  Google Scholar 

  8. M. M. Malamud and S. M. Malamud, “Operator measures in a Hilbert space,” Alg. Analiz, 15, No. 3, 1–52 (2003).

    MathSciNet  Google Scholar 

  9. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in a Hilbert Space [in Russian], Gostekhteorizdat, Moscow (1950).

    Google Scholar 

  10. Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  11. M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in a Hilbert Space [in Russian], Leningrad University, Leningrad (1980).

    Google Scholar 

  12. M. H. Stone, Linear Transformations in Hilbert Space and Their Applications to Analysis, American Mathematical Society, Providence, RI (1932).

    Google Scholar 

  13. N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis [in Russian], Fizmatgiz, Moscow (1961).

    MATH  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 4, pp. 471–482, April, 2010.

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Zagorodnyuk, S.M. On the strong matrix Hamburger moment problem. Ukr Math J 62, 537–551 (2010). https://doi.org/10.1007/s11253-010-0370-2

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