Dual of the function algebra 𝐴^{-∞}(𝐷) and representation of functions in Dirichlet series

Abanin, A.; Khoi, Le

doi:10.1090/S0002-9939-10-10383-9

Dual of the function algebra $A^{-\infty }(D)$ and representation of functions in Dirichlet series
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by A. V. Abanin and Le Hai Khoi PDF

Proc. Amer. Math. Soc. 138 (2010), 3623-3635 Request permission

Abstract:

In this paper we present the following results: a description, via the Laplace transformation of analytic functionals, of the dual to the (DFS)-space $A^{-\infty }(D)$ ($D$ being either a bounded $C^2$-smooth convex domain in $\mathbb {C}^N$, with $N>1$, or a bounded convex domain in $\mathbb {C}$) as an (FS)-space $A^{-\infty }_D$ of entire functions satisfying a certain growth condition; an explicit construction of a countable sufficient set for $A^{-\infty }_D$; and a possibility of representating functions from $A^{-\infty }(D)$ in the form of Dirichlet series.

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