Abstract
The behavior of the Dirichlet series with null abscissa of absolute convergence is studied on semistrips.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Polya, “Untersuchungen über Lücken und Singularitäten von Potenzreihen,”Math. Z.,29, 549–640 (1929).
A. F. Leont'ev,Series of Exponents [in Russian], Nauka, Moscow (1976).
A. F. Leont'ev,Sequences of Polynomials of Exponents [in Russian], Nauka, Moscow (1980).
M. N. Sheremeta, “The growth of entire functions represented by Dirichlet series on a semistrip,”Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 3, 674–687 (1981).
V. A. Martirosyan, “On entire functions that are bounded on a closed angle and representable by the power series with gaps or with real coefficients,”Dokl. Akad. Nauk SSSR,290, No. 6, 1301–1304 (1986).
A. M. Gaisin, “An estimate of the growth rate on a semistrip for a function represented by the Dirichlet series,”Mat. Sb.,117, No. 3, 412–424 (1982).
A. M. Gaisin, “The behavior of the sum of Dirichlet series on semistrips,”Mat. Zametki,42, 660–669 (1987).
P. Turan,Eine neue Methode in der Analysis und deren Anwendungen, Budapest (1953).
M. N. Sheremeta, “Analogs of Wiman's theorem for Dirichlet series,”Mat. Sb.,110, No. 1, 102–116 (1979).
O. B. Skaskiv, “The behavior of the maximal term of Dirichlet series determining an entire function,”Mat. Zametki,37, 41–47 (1985).
P. Rosenbloom, “Probability and entire functions,” in:Studies in Mathematical Analysis and Related Topics, California University Press, Stanford (1962).
T. Kövari, “On the maximum modulus and maximum term of functions analytic in unit disc,”J. London Math. Soc.,41, No 1, 129–137, (1966).
N. M. Suleimanov, “Estimates of Wiman-Valiron type for power series with finite radius of convergence and their accuracy,”Dokl. Akad. Nauk SSSR,253, No. 4, 822–825 (1980).
Yu. M. Gal', “On analogs of the Wiman-Valiron theorem for Dirichlet series whose exponents have positive step,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 57–59 (1986).
F. I. Geche and S. V. Onipchuk, “On abscissae of convergent Dirichlet series and its Newton majorant,”Ukr. Mat. Zh.,26, No. 2, 161–168 (1974).
O.B. Skaskiv and V.M. Sorokivskii, “The growth on horizontal rays of analytic functions represented by the Dirichlet series,”Ukr. Mat. Zh.,42, No. 3, 363–371 (1990).
V. M. Sorokivs'kii, “The behavior of analytic functions defined by Dirichlet series on a semistrip,”Visn. L'viv. Univ., Ser. Mekh.-Mat., Issue 24, 40–43 (1985).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 681–693, May, 1993.
Rights and permissions
About this article
Cite this article
Skaskiv, O.B. On the growth of analytic functions represented by the Dirichlet series on semistrips. Ukr Math J 45, 745–760 (1993). https://doi.org/10.1007/BF01058210
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058210