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

Authors: A. V. Abanin and Le Hai Khoi
Journal: Proc. Amer. Math. Soc. 138 (2010), 3623-3635
MSC (2010): Primary 32A38, 46A13
Published electronically: May 7, 2010
MathSciNet review: 2661561
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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)$ ($ 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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Additional Information

A. V. Abanin
Affiliation: Southern Institute of Mathematics, Southern Federal University, Rostov-on-Don 344090, The Russian Federation

Le Hai Khoi
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore

Keywords: Function algebra, dual space, Laplace transformation, sufficient set, Dirichlet series
Received by editor(s): June 14, 2009
Received by editor(s) in revised form: January 8, 2010
Published electronically: May 7, 2010
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society

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