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.
Similar content being viewed by others
References
A. Baernstein, Proof of Edrei’s spread conjecture, Proc. London Math. Soc. (3) 26 (1973), 418–434.
A. Baernstein, A generalization of the cosπρ theorem, Trans. Amer. Math. Soc. 193 (1974), 181–197.
K. Barth, D. Brannan and W. K. Hayman, Research problems in complex analysis, Bull. London Math. Soc. 16 (1984), 490–517.
D. Drasin and D. Shea, Convolution inequalities, regular variation and exceptional sets, J. Analyse Math. 29 (1976), 232–293.
P. C. Fenton and J. Rossi, A reverse Denjoy theorem, Bull. London Math. Soc. 41 (2009), 27–35.
P. C. Fenton and J. Rossi, A reverse Denjoy theorem II, J. Analyse Math. 110 (2010), 385–395.
P. C. Fenton and J. Rossi, A reverse Denjoy theorem III, Science China Mathematics 53 (2010), 657–662.
A. Fryntov, Subharmonic functions and cos πλ-theorems for entire functions represented by gap series, Adv. Soviet Math. 11 (1992), 205–222.
A. Fryntov, On behaviour of gap series on curves and a cos πλ-type theorem, Complex Variables 37 (1998), 195–208.
T. Kövari, On the growth of entire functions of finite order with density conditions, Quart. J. Math. Oxford Ser. (2) 17 (1966), 22–30.
J. Rossi and J. Williamson, The asymptotic behavior of functions extremal for Baernstein’s cosαλ theorem, J. Analyse Math. 42 (1983), 128–154.
J. Rossi, The radial growth of entire functions with density conditions, Complex Variables 22 (1993), 175–180.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321820