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
- Proc. Amer. Math. Soc. 138 (2010), 3623-3635
- DOI: https://doi.org/10.1090/S0002-9939-10-10383-9
- Published electronically: May 7, 2010
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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.References
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Bibliographic Information
- A. V. Abanin
- Affiliation: Southern Institute of Mathematics, Southern Federal University, Rostov-on-Don 344090, The Russian Federation
- Email: abanin@math.rsu.ru
- Le Hai Khoi
- Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
- MR Author ID: 262091
- Email: lhkhoi@ntu.edu.sg
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 3623-3635
- MSC (2010): Primary 32A38, 46A13
- DOI: https://doi.org/10.1090/S0002-9939-10-10383-9
- MathSciNet review: 2661561