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On convergence classes of Dirichlet series

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Abstract

We establish conditions for the coefficients of a Dirichlet series under which this series belongs to a certain class of convergence.

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References

  1. G. Valiron,General Theory of Integral Functions, Toulouse (1923).

  2. P. K. Kamthan, “A theorem of step functions. II,”Istanbul Univ. Fen. Fac. Mecm. A.,28, 65–69 (1963).

    MATH  MathSciNet  Google Scholar 

  3. Yu. M. Gal’ and M. N. Sheremeta, “On the property of analytic functions to belong to a certain class of convergence,”Dop. Akad. Nauk Mr. SSR, Ser. A, No. 7, 11–14 (1985).

    Google Scholar 

  4. G. H. Hardy, J. E. Littlewood, and G. Pólya,Inequalities [Russian translation], Inostrannaya Literatura, Moscow (1948).

    Google Scholar 

  5. A. F. Leont’ev,Exponential Series [in Russian], Nauka, Moscow (1976).

    MATH  Google Scholar 

  6. M. N. Sheremeta, “Binomial asymptotics of entire Dirichlet series,”Teor. Funkts., Funkts. Anal. Prilozh., Issue 54, 16–25 (1990).

    Google Scholar 

  7. M. N. Sheremeta,Entire Dirichlet Series [in Ukrainian], ISDO, Kiev (1993).

    Google Scholar 

  8. B. V. Vinnitskii and M. N. Sheremeta, “On the coefficients of a Dirichlet series that determines an entire function,”Ukr. Mat. Zh.,29, No. 2, 232–237 (1977).

    Article  MATH  Google Scholar 

  9. M. N. Sheremeta, Ya. Ya. Pritula, and S. I. Fedynyak,Growth of Dirichlet Series [in Ukrainian], Preprint No. 18–95, Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lvov (1995).

    Google Scholar 

  10. M. N. Sheremeta, “On the relationship between the growth of the maximum of modulus of an entire function and the moduli of the coefficients of its power expansion,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 100–108 (1967).

    Google Scholar 

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Authors and Affiliations

  1. Drogobych Pedagogical Institute, Drogobych

    O. M. Mulyava

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  1. O. M. Mulyava
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1485–1494, November, 1999.

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Mulyava, O.M. On convergence classes of Dirichlet series. Ukr Math J 51, 1681–1692 (1999). https://doi.org/10.1007/BF02525271

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  • DOI: https://doi.org/10.1007/BF02525271

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