Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): A. V. Abanin; Le Hai Khoi
Journal: Proc. Amer. Math. Soc. 138 (2010), 3623-3635.
MSC (2010): Primary 32A38, 46A13
Posted: May 7, 2010
MathSciNet review: 2661561
Retrieve article in: PDF

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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 $A^{-\infty}(D)$ ( being either a bounded -smooth convex domain in $\mathbb{C}^N$ , with , 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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