Certain results on a class of integral functions represented by multiple Dirichlet series. (English) Zbl 1474.30019

Summary: In the present paper we obtain a condition on vector valued coefficients of multiple Dirichlet series for when the series converges in the whole complex plane. We also prove some results related to Banach algebraic structure, topological divisor of zero and more on a class of such series satisfying certain condition.


30B50 Dirichlet series, exponential series and other series in one complex variable
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
17A35 Nonassociative division algebras
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[1] A.I. Janusauskas,Elementary theorems on the convergence of double Dirichlet series, Dokl. Akad. Nauk. SSSR,234(1977), 610-614. (in Russian) · Zbl 0388.40003
[2] N. Kumar, G. Manocha,A class of entire Dirichlet Series as an FK-space and a Frechet space, Acta Mathematica Scientia,33B(6)(2013), 1571-1578. · Zbl 1313.30007
[3] N. Kumar, L. Chutani, G. Manocha,Certain results on a class of entire Dirichlet series in two variables, Scientia Magna,11(2)(2016), 33-40.
[4] P. K. Sarkar,On Gol’dberg order and Gol’dberg type of an entire function of several complex variables represented by multiple Dirichlet series, Indian J. Pure Appl. Math.,13(10)(1982), 1221-1229. · Zbl 0513.32005
[5] R.K. Srivastava,Some growth properties of a class of entire Dirichlet series, Proc. Nat. Acad. Sci. India,61(A)(1991), 507-517 IV. · Zbl 0885.30004
[6] R. Larsen,Banach Algebras - An Introduction, Marcel Dekker Inc., New York 1973. · Zbl 0264.46042
[7] R. Larsen,Functional Analysis - An Introduction, Marcel Dekker Inc., New York 1973. · Zbl 0261.46001
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