Existence Theorems for Multidimensional Generalized Moment Representations

We establish the conditions for the existence of multidimensional generalized moment representations.

References

  1. 1.

    V. K. Dzyadyk, “On the generalization of the problem of moments,” Dop. Akad. Nauk Ukr. RSR, 6, 8–12 (1981).

    MATH  Google Scholar 

  2. 2.

    A. P. Holub, Generalized Moment Representations and Padé Approximations [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2002).

  3. 3.

    V. K. Dzyadyk and A. P. Golub, Generalized Problem of Moments and the Padé Approximation [in Russian], Preprint No. 81.58, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1981), pp. 3–15.

  4. 4.

    A. P. Golub, “Existence theorems for generalized moment representations,” Ukr. Mat. Zh., 55, No. 7, 881–888 (2003); English translation : Ukr. Math. J., 55, No. 7, 1061–1070 (2003).

  5. 5.

    A. P. Holub and L. O. Chernets’ka, “Two-dimensional generalized moment representations and rational approximations of functions of two variables,” Ukr. Mat. Zh., 65, No. 8, 1035–1058 (2013); English translation : Ukr. Math. J., 65, No. 8, 1155–1179 (2014).

  6. 6.

    A. P. Holub and L. O. Chernets’ka, “Many-dimensional generalized moment representations and Padé-type approximants for functions of many variables,” Ukr. Mat. Zh., 66, No. 9, 1166–1174 (2014); English translation : Ukr. Math. J., 66, No. 9, 1302–1311 (2015).

  7. 7.

    Yu. L. Ershov, Numbering Theory [in Russian], Nauka, Moscow (1977).

  8. 8.

    F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).

  9. 9.

    D. Z. Arov, “Passive linear stationary dynamical systems,” Sib. Mat. Zh., 20, No. 2, 211–228 (1979).

  10. 10.

    G. V. Radzievskii, “Existence theorems for the Dzyadyk generalized moment representations,” Mat. Zametki, 75, No. 2, 253–260 (2004).

  11. 11.

    B. A. Fuks, Introduction to the Theory of Analytic Functions of Many Complex Variables [in Russian], Fizmatgiz, Moscow (1962).

  12. 12.

    P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Springer, Berlin (1986).

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Correspondence to H. M. Veselovs’ka.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 4, pp. 456–465, April, 2017.

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Veselovs’ka, H.M., Holub, A.P. Existence Theorems for Multidimensional Generalized Moment Representations. Ukr Math J 69, 534–545 (2017). https://doi.org/10.1007/s11253-017-1380-0

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