American Journal of Mathematical Analysis. 2019, 7(1), 11-14
DOI: 10.12691/ajma-7-1-2
Open AccessArticle
Niraj Kumar1, and Lakshika Chutani1
1Department of Mathematics, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi-110078, India
Pub. Date: November 17, 2019
Cite this paper:
Niraj Kumar and Lakshika Chutani. A Study on a Class of Entire Dirichlet Series in n - Variables. American Journal of Mathematical Analysis. 2019; 7(1):11-14. doi: 10.12691/ajma-7-1-2
Abstract
In this paper a class L of entire functions represented by Dirichlet series in n variables has been considered whose coefficients belong to the set of complex numbers C and is further proved to be a Banach Algebra. Also characterization of continuous linear functional is done for the set L.Keywords:
Dirichlet series Banach algebra topological zero divisor division algebra continuous linear functionalThis implies
This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit
http://creativecommons.org/licenses/by/4.0/
References:
[1] | Janusauskas A.I., 1977. Elementary theorems on convergence of double Dirichlet series. Dokl. Akad. Nauk. SSSR, 234, 610-614. |
|
[2] | Sarkar P.K., 1982. On the Goldberg order and Goldberg type of an entire function of several complex variables represented by multiple Dirichlet series. Indian J. Pure Appl. Math. 13(10), 1221-1229. |
|
[3] | Meili L., Zongsheng G., 2010. Convergence and Growth of multiple Dirichlet series. Acta Mathematica Scientia. 30B(5), 1640-1648. |
|
[4] | Vaish S.K., 2003. On the coe_cients of entire multiple Dirichlet series of several complex variables. Bull. Math. Soc. Sc. Roumanie Tome. 46(94) 3-4, 195-202. |
|
[5] | Kumar N., Manocha G., 2013. On a class of entire functions represented by Dirichlet series. J. Egypt. Math. Soc. 21, 21-24. |
|
[6] | Kumar N., Manocha G., 2013. A class of entire Dirichlet series as an FK-space and a Frechet space. Acta Math. Scientia. 33B(6), 1571-1578. |
|
[7] | Larsen R., 1973. Banach Algebras - An Introduction. Marcel Dekker Inc., New York. |
|
[8] | Larsen R., 1973. Functional Analysis - An Introduction. Marcel Dekker Inc., New York. |
|