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On the solvability of one class of differential equations of infinite order

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Literature Cited

  1. 1.

    B. Ya. Lovin, Distribution of the Roots of Entire Functions [in Russian], GTTI, Moscow (1956).

  2. 2.

    A. F. Leont'ev, Differential-Difference Equations with Linear Coefficients, Trudy Gor'kovsk. ped. in-ta, Fiz.-Matem., Issue 14,3, 3–30 (1951).

  3. 3.

    A. A. Mirolyubov, Solution of Differential-Difference Equations with Linear Coefficienis, Matem. Sb.,34, No. 2, 357–335 (1954).

  4. 4.

    A. A. Mirolyubov, Solution of Differential-Difference Equations with Polynomial Coefficients, Matem. Sb.,42, No. 1, 65–78 (1957).

  5. 5.

    M. A. Kraplin, On Entire and Meromorphic Solutions of Difference Equations with Polynomial Coefficients [in Russian], Candidate's Dissertation, Rostov State University (1962).

  6. 6.

    A. G. Naftalevich, On Application of the Method of Iterations for the Solution of a Difference Equation, Matem. Sb.,57, No. 2, 151–179 (1962).

  7. 7.

    Yu. F. Korobeinik, On Entire Analytic Solutions of an Equation of Infinite Order with Polynomial Coefficients, Dokl. Akad. Nauk SSSR,157, No. 5, 1031–1034 (1964).

  8. 8.

    F. V. Atkinson, normal Solvability of Linear Equations in Normalized Spaces, Matem. Sb.,28, No. 1, 3–14 (1951).

  9. 9.

    M. G. Krein, Integral Equations on a Half-Line with Kernel Depending on a Difference of Arguments, Uspekhi Matem. Nauk,XIII, No. 5, 3–121 (1958).

  10. 10.

    M. G. Krein and I. Ts. Gokhberg, Fundamental Assumptions About Imperfect Numbers, Radical Numbers, and the Indices of Linear Operators, Uspekhi Matem. Nauk,XII, No. 2, 43–119 (1957).

  11. 11.

    J. Dieudonne and L. Schwartz, La Dualite dans les Espaces (F) et (LF), Ann. Inst. Fourier (Grenoble),1 (1950), pp. 61–101.

  12. 12.

    Yu. F. Korobeinik, Analytic Solutions of Operator Equations of Infinite Order [in Russian], Doctoral Dissertation, Rostov State University (1965).

  13. 13.

    L. V. Kantorovich and G. P. Akilov, Functional Analysis and Normalized Spaces [in Russian], Fizmatgiz, Moscow (1959).

  14. 14.

    N. Bourbaki, Topological Vector Spaces [Russian translation], IL, Moscow (1959).

  15. 15.

    G. Vittikh, Latest Investigations with Regard to Single-Velued Analytic Functions [in Russian], Fizmatgiz, Moscow (1960).

  16. 16.

    Zh. Valiron, Analytic Functions [in Russian], GITTL, Moscow (1957).

  17. 17.

    M. G. Khaplanov, Linear Differential Equations of Infinite Order with Analytic Coefficients, Dokl. Akad. Nauk SSSR,105, No. 6, 1162–1165 (1955).

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Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 8, No. 6, pp. 1321–1338, November–December, 1967.

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Korobeinik, Y.F., Demchenko, T.I. On the solvability of one class of differential equations of infinite order. Soviet Mathematical Journal 8, 1004–1015 (1967).

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  • Differential Equation
  • Infinite Order