Skip to main content
Log in

Asymptotics of Blaschke Products the Counting Function of Zeros of Which Is Slowly Increasing

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We find the asymptotics as z→ 1 for the Blaschke product with positive zeros the counting function of which n(t) is slowly increasing, i.e., n((t+ 1)/2) ∼ n(t) as t→ 1.

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.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. G. Valiron, “Sur les fonctions entiéres dórdre nul et dórdre fini et en particulier les fonctions á correspondance réguliére,” Ann. Fac. Sci. Univ. Toulouse, 5, 117–257 (1914).

    Google Scholar 

  2. E. G. Titchmarsh, “On integral functions with real negative zeros,” Proc. London Math. Soc., 26, 185–200 (1927).

    Google Scholar 

  3. M. A. Girnyk, “On asymptotic properties of certain canonical products,” Sib. Mat. Zh., 25, No.5, 1036–1048 (1974).

    Google Scholar 

  4. R. S. Galoyan, “On asymptotic properties of the functions πz; z k,” Dokl. Akad. Nauk Arm. SSR, 59, No.2, 65–71 (1974).

    Google Scholar 

  5. M. V. Zabolots'kyi, “Valiron-type and Valiron–Titchmarsh-type theorems for entire functions of order zero,” Ukr. Mat. Zh., 48, No.3, 315–325 (1996).

    Google Scholar 

  6. A. A. Gol'dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions[in Russian], Nauka, Moscow (1970).

    Google Scholar 

  7. E. Seneta, Regularly Varying Functions[Russian translation], Nauka, Moscow (1985).

    Google Scholar 

  8. J. B. Garnett, Bounded Analytic Functions[Russian translation], Mir, Moscow (1984).

    Google Scholar 

  9. M. O. Ghirnyk and A. A. Kondratyuk, “Blaschke products of given quantity index,” Mat. Stud., Issue 2, 49–52 (1993).

    Google Scholar 

  10. A. A. Shkalikov, “Tauberian-type theorems on distribution of zeros of holomorphic functions,” Mat. Sb., 123, No.3, 317–347 (1984).

    Google Scholar 

  11. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series[in Russian], Nauka, Moscow (1981).

    Google Scholar 

  12. G. M. Fikhtengol'ts, A Course of Differential and Integral Calculus[in Russian], Vol. 2, Nauka, Moscow (1970).

    Google Scholar 

  13. V. N. Logvinenko, “On entire functions with zeros on a half-line,” Teor. Funkts., Funkts. Anal. Prilozh., Issue 17, 84–99 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zabolots'kyi, M.V. Asymptotics of Blaschke Products the Counting Function of Zeros of Which Is Slowly Increasing. Ukrainian Mathematical Journal 52, 1882–1895 (2000). https://doi.org/10.1023/A:1010455926490

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010455926490

Keywords

Navigation