Mushtaq Shaker Abdul-Hussein and G.S. Srivastava A STUDY OF BORNOLOGICAL PROPERTIES OF THE SPACE OF ENTIRE FUNCTIONS REPRESENTED BY MULTIPLE DIRICHLET SERIES
نویسنده
چکیده
The space of entire functions represented by Dirichlet series of several complex variables has been studied by S. Dauod [1]. M.D. Patwardhan [6] studied the bornological properties of the space of entire functions represented by power series. In this work we study the bornological aspect of the space Γ of entire functions represented by Dirichlet series of several complex variables. By Γ we denote the space of all analytic functions α(s1, s2) = ∞ ∑ m,n=1 am,n exp(λms1 + μns2), having finite abscissa of convergence. We introduce bornologies onΓ and Γ, and prove that Γis a convex bornological vector space which is the completion of the convex bornological vector space Γ.
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