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Consider the space $L$ of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space $L$ the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained.

On entire Dirichlet series of order (R) infinity

P. K. Jain (1971)

Matematički Vesnik

On Entire Functions Represented by Dirichlet Series.

Pawan Kumar Kamthan (1964)

Monatshefte für Mathematik

On Regularly Varying Functions With Applications To Functions Theory.

O.P. Juneja, G.S. Srivastava (1981)

Revista colombiana de matematicas

On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

On the Lower Order of an Entire Dirichlet Series.

O.P. Juneja, G.P. Kapoor (1972)

Mathematische Annalen

On the lower order $(R)$ of an entire Dirichlet series

P. K. Jain, D. R. Jain (1974)

Annales de l'institut Fourier

The estimations of lower order $(R)$ $λ$ in terms of the sequences ${a_{n}}$ and ${λ_{n}}$ for an entire Dirichlet series $f (s) = \sum_{n = 1}^{\infty} a_{n} e^{s λ n}$ , have been obtained, namely : $\begin{matrix} λ & = max_{{λ_{n_{p}}}} lim inf_{p \to \infty} \frac{λ_{n_{p}} log λ_{n_{p - 1}}}{log | a_{n_{p}} |^{- 1}} \\ = max_{{λ_{n_{p}}}} lim inf_{p \to \infty} \frac{(λ_{n_{p}} - λ_{n_{p - 1}}) log λ_{n_{p - 1}}}{log | a_{n_{p - 1}} | a_{n_{p}} |} . \end{matrix}$ One of these estimations improves considerably the estimations earlier obtained by Rahman (Quart. J. Math. Oxford, (2), 7, 96-99 (1956)) and Juneja and Singh (Math. Ann., 184(1969), 25-29 ).

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Generalized quadratic mean Functions of Entire Functions Defined by Dirichlet Series

Growth numbers of Entire Functions Defined by Dirichlet Series

Growth of solutions to higher order linear homogeneous differential equations in angular domains.

Hermite interpolation and an inequality for entire functions of exponential type.

Holomorphic extension of a function whose odd derivatives are summable

Integral representation of a solution of Heun's general equation.

Logarithmic Mean Of An Entire Dirchlet Series

Maximum modulus function of derivatives of entire functions defined by Dirichlet series

On a converse of Laguerre's theorem.

On an entire function represented by multiple Dirichlet series

On entire Dirichlet series of order (R) infinity

On Entire Functions Represented by Dirichlet Series.

On Regularly Varying Functions With Applications To Functions Theory.

On the growth of an algebroid function with radially distributed values

On the Lower Order of an Entire Dirichlet Series.

On the lower order $(R)$ of an entire Dirichlet series

On the maximum term and maximum modulus of analytic functions represented by Dirichlet series

On the Maximum Term of an Integral Function and Its Derivatives (II).

On the mean of entire functions defined by Dirichlet series with index (p,q)

On the mean values of an entire Dirichlet series of order zero

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