We solve the problem of estimation of growth for the maximum modulus of an entire function of bounded L -index in a direction. Some generalizations of the earlier one-dimensional results are obtained.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. I. Bandura and O. B. Skaskiv, “Entire functions of bounded L -index in a direction,” Mat. Studii, 27, No. 1, 30–52 (2007).
H. Wittich, Neuere Untersuchungen Über Eindeutige Analytische Funktionen, Springer-Verlag, Berlin etc. (1968).
A. D., Kuzyk and M. N. Sheremeta, “Entire functions of bounded ℓ -distribution of values,” Mat. Zametki, 39, No. 1, 3–13 (1986); English translation: Math. Notes, Acad. Sci. USSR, 39, No. 1, 3–8 (1986).
G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Bd. II, Springer-Verlag, Berlin, etc. (1964).
T. O. Banakh and V. O. Kushnir, “On growth and distribution of zeros of analytic functions of bounded ℓ -index in arbitrary domains,” Mat. Studii, 14, No. 2, 165–170 (2000).
A. I. Bandura and O. B. Skaskiv, “Open problems for entire functions of bounded index in direction,” Mat. Stud., 43, No. 1, 103–109 (2015).
B. Lepson, “Differential equations of infinite order, hyper-Dirichlet series and entire functions of bounded index,” in: Entire Functions and Related Parts of Analysis, Proc. Symp. Pure Math., La Jolla, Calif. (1966), Providence, RI.: Amer. Math. Soc., Vol. XI (1968), pp. 298–307.
F. Nuray and R. F. Patterson, “Entire bivariate functions of exponential type,” Bull. Math. Sci., 5, No. 2, 171–177 (2015).
F. Nuray and R. F. Patterson, “Multivalence of bivariate functions of bounded index,” Le Matematiche, 70, No. 2, 225–233 (2015).
S. M. Shah, “Entire functions of bounded index,” Proc. Amer. Math. Soc., 19, No. 5, 1017–1022 (1968).
M. Sheremeta, Analytic Functions of Bounded Index, VNTL Publishers, Lviv (1999), (Math. Studies: Monograph Ser., Vol. 6.).
Author information
Authors and Affiliations
Additional information
Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 1, pp. 22–31, January–March, 2017.
Rights and permissions
About this article
Cite this article
Bandura, A.I., Skaskiv, O.B. Growth of Entire Functions of Bounded L-Index in a Direction. J Math Sci 240, 21–33 (2019). https://doi.org/10.1007/s10958-019-04333-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-019-04333-7