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An interpolation problem in the class of stieltjes functions and its connection with other problems

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This paper contains the proofs and some development of results that were published without proofs in [KN2]. It is completed with comments added by the second author explaining how these results became the basis of statements and the solutions of problems in the theory of entire functions, in the moment problem, in direct and inverse problems of the spectral theory of nonhomogeneous strings and in other problems.

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References

  1. N. I. Akhiezer,On a generalization of the Fourier transform and the Wiener-Paley theorem, Doklady Akad. Nauk SSSR, 454 (1954), vol. 96, 889–892 (Russian).

    Google Scholar 

  2. F. V. Atkinson,Discrete and continuous boundary problems, Academic Press, New York, 1964; Russian transl.: “Mir”, Moscow, 1968.

    Google Scholar 

  3. H. Dym, H. P. McKean,Gaussian processes, function theory and the inverse spectral problems, Academic Press, New York, 1976.

    Google Scholar 

  4. V. P. Gurariî,A generalization of the Fourier transform and of the Wiener-Paley theorem, Doklady Akad. Nauk SSSR, 1960, vol. 130, 959–962 (Russian).

    Google Scholar 

  5. I. G. Kaplan,Introduction in the theory of molecular interactions, Moscow, “Nauka”, 1982 (Russian).

    Google Scholar 

  6. I. S. Kac, M. G. Krein,R-functions — analytic functions mapping upper half-plane into itself, Supplement I of the Russian translation of [At]; Engl.trans.: AMS Transl. (2), vol. 103, 1974, 1–18.

    Google Scholar 

  7. I. S. Kac, M. G. Krein,On the spectral functions of the string, Supplement II of the Russian translation of [At]; Engl. transl.: AMS Transl. (2), vol. 103, 1974, 19–102.

    Google Scholar 

  8. M. G. Krein, B. Ya. Levin, A. A. Nudelman,On a special representation of polynomials that are positive on a system of closed intervals, Preprint No 28-84. Fiz.-Tekh. Inst. Nizkikh Temperatur Akad. Nauk Ukrain. SSR, Kharkov, 1984, 1–48; Engl. transl.: AMS Transl. (2), vol. 142, 1989, 33–40.

    Google Scholar 

  9. M. G. Krein, B. Ya. Levin, A. A. Nudelman,On a special representation of polynomials that are positive on a system of closed intervals and some applications, Functional analysis, optimization and mathematical economics, Ed. L. Leifman, Oxford Univ. Press, 1990, 56–114.

  10. M. G. Krein, A. A. Nudelman,The Markov moment problem and extremal problems, Moscow, “Nauka”, 1973 (Russian); Engl. Transl.: AMS Transl. Math. Monographs, vol. 50, 1977; Providence, RI, 1977

    Google Scholar 

  11. M. G. Krein, A. A. Nudelman,On an interpolation problem related to the Stieltjes moment problem, Doklady Akad. Nauk Ukrainian SSR, Serie A, 1977, No 12, 1068–1072 (Russian and Ukranian).

    Google Scholar 

  12. M. G. Krein, A. A. Nudelman,On direct and inverse problems for the boundary dissipation frequencies of a nonuniform string, Doklady Akad. Nauk SSSR, vol. 247, 1979, N 5, 1046–1049 (Russian); Engl. transl.: Soviet Math. Dokl., vol.20 (1979), No 4, 838–841.

    Google Scholar 

  13. M. G. Krein, A. A. Nudelman,On representation of entire functions positive on the real axis, or on semiaxis or outside a finite interval, Linear operators and integral equations, Chisinău, vol. 61, 1981, 40–59 (Russian); Engl. transl.: AMS Transl. (2), vol. 127, 1986, 17–31.

    Google Scholar 

  14. M. G. Krein, A. A. Nudelman,Some propositions on the theorems of Fourier-Plancherel and Wiener-Paley type obtained by methods of the spectral functions theory, Functional Analysis and its Applications, vol. 13 (1979), N4, 79–90 (Russian).

    Google Scholar 

  15. M. G. Krein, A. A. Nudelman,On some spectral properties of an nonhomogenous string with a dissipative boundary condition, Journ. of Operator Theory, Vol. 22, 1989, 369–395 (Russian).

    Google Scholar 

  16. M. G. Krein,On a generalization of investigations of Stieltjes, Doklady Akad. Nauk SSSR, vol. 87 (1952), 881–884 (Russian).

    Google Scholar 

  17. A. A. Nudelman, A. V. Tulub,Some extremal problems in the theory of the Vander-Waals forces, Teoreticheskaya i matematicheskaya fizika, vol. 39, No 3, 1979, 359–367 (Russian).

    Google Scholar 

  18. A. A. Nudelman,Multipoint matrix moment problem, Doklady Akad. Nauk SSSR, vol. 298, 1988, 812–815 (Russian).

    Google Scholar 

  19. A. A. Nudelman,Matrix versions of interpolation problems of Nevanlinna-Pick and Loewner type, Systems and Networks: Math. theory and Appl., vol. 1 (1994), 291–310.

    Google Scholar 

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Authors and Affiliations

  1. ul. Balkovskaya, 141/187, 270005, Odessa, Ukraine

    A. A. Nudelman

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  1. M. G. Krein
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  2. A. A. Nudelman
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Krein, M.G., Nudelman, A.A. An interpolation problem in the class of stieltjes functions and its connection with other problems. Integr equ oper theory 30, 251–278 (1998). https://doi.org/10.1007/BF01195584

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  • DOI: https://doi.org/10.1007/BF01195584

MSC 1991

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