Skip to main content
SpringerLink
Log in

Entire functions with a given sequence of zeros and of regular behavior on the real axis. I

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We demonstrate that if a sequence of positive numbers increasing to infinity has S-density then it can be prolonged to some sequence that is the zero set of the Weierstrass product of regular behavior on the real axis.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Leont’ev A. F., Series of Exponentials [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  2. Redheffer R. M., “Completeness of sets of complex exponentials,” Adv. Math., 24, No. 1, 1–62 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  3. Katsnel’son V. É., “Entire functions of the Cartwright class with irregular behavior, ” Funktsional. Anal. i Prilozhen., 10, No. 4, 35–44 (1976).

    MATH  Google Scholar 

  4. Matsaev V. I., History of Soviet Mathematics. Vol. 4, Part 1 [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  5. Koosis P., The Logarithmic Integral. I, Cambridge University Press, Cambridge (1988).

    Google Scholar 

  6. Leont’ev A. F., “On the convergence of a sequence of Dirichlet polynomials,” Dokl. Akad. Nauk SSSR, 108, No. 1, 23–26 (1956).

    MATH  MathSciNet  Google Scholar 

  7. Baillette A., “Approximation de fonctions par des sommes d’exponentielles,” C. R. Acad. Sci. Paris Sér. I Math., 249, No. 23, 2470–2471 (1959).

    MATH  MathSciNet  Google Scholar 

  8. Leont’ev A. F., Sequences of Exponential Polynomials [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa, Russia

    A. M. Gaisin & D. I. Sergeeva

Authors
  1. A. M. Gaisin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. I. Sergeeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Gaisin.

Additional information

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 995–1007, September–October, 2007.

Original Russian Text Copyright © 2007 Gaĭsin A. M. and Sergeeva D. I.

The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00417-a).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaisin, A.M., Sergeeva, D.I. Entire functions with a given sequence of zeros and of regular behavior on the real axis. I. Sib Math J 48, 798–808 (2007). https://doi.org/10.1007/s11202-007-0082-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-007-0082-5

Keywords

Search

Navigation