Skip to main content
Log in

Distribution of indices of representing systems of generated exponents

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. Yu. F. Korobeinik, “Representing systems,” Usp. Mat. Nauk,36, No. 1, 73–126 (1981).

    Google Scholar 

  2. A. F. Leont'ev, Series of Exponents [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  3. A. F. Leont'ev, Generalizations of Exponent Series [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  4. Yu. F. Korobeinik, “Inductive and projective topologies. Sufficient sets and representing systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 3, 539–565 (1986).

    Google Scholar 

  5. G. M. Pasechnik, “Geometric characterization of a set of indices of representing systems of exponents for the space H(G),” Dokl. Akad. Nauk SSSR,252, No. 3, 553–555 (1980).

    Google Scholar 

  6. A. V. Abanin, “On the distribution of efficient sets and inside-continuity of the representing Mittag-Leffler systems,” Mat. Zametki,33, No. 5, 657–668 (1983).

    Google Scholar 

  7. D. M. Schneider, “Sufficient sets for some spaces of entire functions,” Trans. Am. Math. Soc.,197, 161–180 (1974).

    Google Scholar 

  8. B. Ya. Levin, Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  9. V. A. Tkachenko, “On operators which commute with generalized differentiation in spaces of analytic functionals with a given growth indicator,” Mat. Sb.,102, (144), No. 3, 435–456 (1977).

    Google Scholar 

  10. O. V. Epifanov, “Differential oeprator with polynomial coefficients in classes of entire functions with a given indicator bound,” Mat. Sb.,114, (156). No. 1, 85–109 (1981).

    Google Scholar 

  11. A. A. Kondratyuk, “Entire functions with a finite maximal density of zeros. 1,” Teor. Punkts., Punkts. Anal. Prilozh.,10, Kharkov University Press (1970), pp. 57–70.

  12. A. V. Bratishchev, “Sufficient conditions for itnerpolarability of sets in classes of entire functions characterized by an indicator,” Dokl. Akad. Nauk SSSR,274, No. 5, 1036–1039 (1984).

    Google Scholar 

  13. M. M. Dzhbashyan, Integral Transformations and Representation of Functions in the Complex Domain [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  14. P. Z. Agranovich, Indicators of Holomorphic Functionals of Several Variables [in Russian], Dissertation: Candidate of Phys.-Math. Sciences, Kharkov (1978).

  15. A. V. Abanin, “On some criteria of weak convergence,” Mat. Zametki,40, No. 4, 442–454 (1986).

    Google Scholar 

  16. V. S. Azarin, “On rays of a completely regular growth of entire functions,” Mat. Sb.,79, (121). No. 4, 463–476 (1969).

    Google Scholar 

  17. V. N. Logvinenko, “Construction of an entire fucntion with a given idnicator for a given integral refined order,” Funkts. Anal. Prilozh.,6, No. 4, 87–88 (1972).

    Google Scholar 

  18. Yu. F. Korobeinik, “Interpolation problems, nontrivial decompositions of zero and representing systems,” Izv. Akad. Nauk USSR, Ser. Mat.,44, No. 5, 1066–1114 (1980).

    Google Scholar 

  19. Yu. F. Korobenik, “On the problem of representing systems,” in: Current Problems of Mathematical Analysis [in Russian], Rostov University Press, Rostov (1978), pp. 100–111.

    Google Scholar 

  20. V. V. Napalkov, “On discrete weakly sufficient sets in some spaces of entire functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 5, 1088–1099 (1981).

    Google Scholar 

  21. A. V. Bratishchev, “A type of lower bounds on entire fucntions of finite order and some applications,” Izv. Akad. Nauk SSSR. Ser. Mat.48, No. 3, 451–475 (1984).

    Google Scholar 

  22. Yu. I. Mel'nik, “On the problem of representing regular functions by Dirichlet series,” Mat. Zametki,21, No. 5, 641–652 (1977).

    Google Scholar 

  23. N. I. Rakhimkulov, Sufficient Sets for Spaces of Entire Functions; Representation of Functions by Exponent Series [in Russian], Dissertation: Candidate of Phys.-Mat. Sciences, Ufa (1984).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 49, No. 2, pp. 3–13, February, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abanin, A.V. Distribution of indices of representing systems of generated exponents. Mathematical Notes of the Academy of Sciences of the USSR 49, 117–124 (1991). https://doi.org/10.1007/BF01137539

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01137539

Navigation