Abstract
In this paper, we study properties of subharmonic functions and entire functions of order zero. We also propose a complete description for closed submodules of some modules of entire functions of order zero.
Similar content being viewed by others
References
A. V. Bratischev and Yu. F. Korobeinik, “On some descriptions of the growth of subharmonic functions,” Mat. Sb., 103, No. 1, 44–65 (1978).
L. Ehrenpreis, “Mean periodic function,” Amer. J. Math., 77, No. 2, 293–326 (1955).
A. A. Goldberg and N. V. Zabolotskii, “The concentration index of a subharmonic function of order zero,” Mat. Zametki, 34, No. 2, 227–236 (1983).
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities [Russian translation], IL, Moscow (1948).
U. Heighman and P. Kennady, Subharmonic Functions [Russian translation], Mir, Moscow (1980).
I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic function spaces. I. Spectral synthesis on convex domains,” Mat. Sb., 87, No. 4, 359–489 (1972).
I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic function spaces. II. Spectral synthesis on convex domains,” Mat. Sb., 88, No. 1 (5), 4–30 (1972).
I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic functions spaces. III. On expansion of spectral synthesis,” Mat. Sb., 88, No. 3 (7), 331–352 (1972).
B. Ya. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence, Rhode Island (1980).
A. I. Markushevich, Theory of Analytic Functions, Vol. 2 [in Russian], Nauka, Moscow (1968).
V. V. Napalkov and I. A. Shagapov, “Closed ideals of some algebras of periodical entire functions,” Dokl. Akad. Nauk SSSR, 354, No. 6, 739–741 (1977).
V. V. Napalkov and I. A. Shagapov, “On invariant subspaces of some spaces of number sequences,” in: Complex Analysis, Nizhni Novgorod State Univ. (1997), pp. 46–50.
G. Sebastian-i-Silva, “On some classes of locally convex spaces important for applications,” Mathematica, 1, No. 1, 60–77 (1957).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.
Rights and permissions
About this article
Cite this article
Napalkov, V.V., Tarov, V.A. On some properties of subharmonic functions and entire functions of order zero. J Math Sci 155, 89–104 (2008). https://doi.org/10.1007/s10958-008-9210-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-008-9210-4