Skip to main content
Log in

On zeros of entire functions of special form

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

Sufficient conditions for an entire function of special form to have no zeros in the open lower half-plane are obtained.

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.

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. E. Lukach, Characteristic Functions (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  3. A. M. Sedletskii, “Entire functions of the S. N. Bernstein class that are not Fourier—Stieltjes transforms,” Mat. Zametki 61(3), 367–380 (1997) [Math. Notes 61 (3–4), 301–312 (1997)].

    MathSciNet  Google Scholar 

  4. I. V. Tikhonov, “Uniqueness theorems in linear nonlocal problems for abstract differential equations,” Izv. Ross. Akad. Nauk. Ser. Mat. 67(2), 133–166 (2003) [Izv.Math. 67 (2), 333–363 (2003)].

    MathSciNet  Google Scholar 

  5. R. M. Trigub and E. S. Belinsky, Fourier Analysis and Approximation of Functions (Klüwer Academic, Boston-Dordrecht-London, 2004).

    MATH  Google Scholar 

  6. G. H. Hardy, “On the zeroes of certain classes of integral Taylor series. Part II. On the integral function,” Proc. London Math. Soc. Ser. 2 2(876), 401–431 (1905).

    Article  Google Scholar 

  7. G. Pólya, “Über die Nullstellen gewisser ganzer Funktionen,” Math. Z. 2(3–4), 352–383 (1918).

    Article  MathSciNet  Google Scholar 

  8. E. C. Titchmarsh, “The zeros of certain integral functions,” Proc. London Math. Soc. Ser. 2 25, 283–302 (1926).

    Article  MathSciNet  Google Scholar 

  9. M. Cartwright, “The zeros of certain integral functions,” Quart. J. Math. 1(1), 38–59 (1930).

    Article  MathSciNet  Google Scholar 

  10. M. Cartwright, “The zeros of certain integral functions. (II),” Quart. J. Math. 2(1), 113–129 (1931).

    Article  MathSciNet  Google Scholar 

  11. A.M. Sedletskii, “On zeros of Laplace transforms of finite measure,” Integral Transform. Spec. Funct. 1(1), 51–59 (1993).

    Article  MathSciNet  Google Scholar 

  12. A.M. Sedletskii, “On the zeros of Laplace transforms,” Mat. Zametki 76(6), 883–892 (2004) [Math. Notes 76 (5–6), 824–833 (2004)].

    MathSciNet  Google Scholar 

  13. V. P. Zastavnyi, “A theorem on the zeros of entire functions and its application,” Mat. Zametki 75(2), 192–207 (2004) [Math. Notes 75 (1–2), 175–189 (2004)].

    MathSciNet  Google Scholar 

  14. V. P. Zastavnyi, “A theorem on zeros of an entire function and its applications,” Methods Funct. Anal. Topology 10(2), 91–104 (2004).

    MATH  MathSciNet  Google Scholar 

  15. N. I. Akhiezer, Lectures on Integral Transformations (Vishcha Shkola, Kharkov, 1984) [in Russian].

    MATH  Google Scholar 

  16. E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces (Princeton Univ. Press, Princeton, NJ, 1971; Mir, Moscow, 1974).

    MATH  Google Scholar 

  17. V. P. Zastavnyi, “On positive definiteness of some functions,” J. Multivariate Anal. 73(1), 55–81 (2000).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. P. Zastavnyi.

Additional information

Original Russian Text © V. P. Zastavnyi, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 1, pp. 24–31.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zastavnyi, V.P. On zeros of entire functions of special form. Math Notes 83, 23–30 (2008). https://doi.org/10.1134/S0001434608010033

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434608010033

Key words

Navigation