Skip to main content
Log in

A Reverse cos πρ Theorem and a Question of Fryntov

  • Published:
Computational Methods and Function Theory Aims and scope Submit manuscript

Abstract

The authors continue their work on reverse Denjoy theorems, proving a reverse cosπρ theorem. The theorem is connected to a question of Fryntov on entire functions with gaps.

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. Baernstein, Proof of Edrei’s spread conjecture, Proc. London Math. Soc. (3) 26 (1973), 418–434.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Baernstein, A generalization of the cosπρ theorem, Trans. Amer. Math. Soc. 193 (1974), 181–197.

    MathSciNet  MATH  Google Scholar 

  3. K. Barth, D. Brannan and W. K. Hayman, Research problems in complex analysis, Bull. London Math. Soc. 16 (1984), 490–517.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Drasin and D. Shea, Convolution inequalities, regular variation and exceptional sets, J. Analyse Math. 29 (1976), 232–293.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. C. Fenton and J. Rossi, A reverse Denjoy theorem, Bull. London Math. Soc. 41 (2009), 27–35.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. C. Fenton and J. Rossi, A reverse Denjoy theorem II, J. Analyse Math. 110 (2010), 385–395.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. C. Fenton and J. Rossi, A reverse Denjoy theorem III, Science China Mathematics 53 (2010), 657–662.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Fryntov, Subharmonic functions and cos πλ-theorems for entire functions represented by gap series, Adv. Soviet Math. 11 (1992), 205–222.

    MathSciNet  Google Scholar 

  9. A. Fryntov, On behaviour of gap series on curves and a cos πλ-type theorem, Complex Variables 37 (1998), 195–208.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Kövari, On the growth of entire functions of finite order with density conditions, Quart. J. Math. Oxford Ser. (2) 17 (1966), 22–30.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Rossi and J. Williamson, The asymptotic behavior of functions extremal for Baernstein’s cosαλ theorem, J. Analyse Math. 42 (1983), 128–154.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Rossi, The radial growth of entire functions with density conditions, Complex Variables 22 (1993), 175–180.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter C. Fenton.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fenton, P.C., Rossi, J. A Reverse cos πρ Theorem and a Question of Fryntov. Comput. Methods Funct. Theory 12, 167–172 (2012). https://doi.org/10.1007/BF03321820

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03321820

Keywords

2000 MSC

Navigation