Bornological spaces of entire functions represented by Dirichlet series having slow growth
Bornological spaces of entire functions represented by Dirichlet series having slow growth
Summary: The study of spaces of entire functions was initiated by \textit{V. G. Iyer} [J. Indian Math. Soc., II. Ser. 12, 13--30 (1948; Zbl 0031.12802)] and the space of entire functions represented by Dirichlet series has been studied by \textit{T. Husain} and \textit{P. K. Kamthan} [Collect. Math. 19, 203--216 (1968; Zbl 0172.40001)] and others. \textit{M. D. Patwardhan} [Indian J. Pure Appl. Math. 12, 865--873 (1981; Zbl 0465.46016)] has successfully studied bornological properties of the spaces of entire functions in terms of the coefficients of Taylor series expansions. In this paper we use another norm and study the bornological aspects of the space \(\Gamma\) of all Dirichlet series \(\alpha(s)=\sum^\infty_{n=1}a_n\exp(s\lambda_n)\) of order zero.
Representations of entire functions of one complex variable by series and integrals, Representations of entire functions by series and integrals, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, Topological linear spaces of continuous, differentiable or analytic functions
Representations of entire functions of one complex variable by series and integrals, Representations of entire functions by series and integrals, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, Topological linear spaces of continuous, differentiable or analytic functions
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