American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2019, 7(1), 11-14
DOI: 10.12691/ajma-7-1-2
Open AccessArticle

A Study on a Class of Entire Dirichlet Series in n - Variables

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

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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.