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A Symbolic Calculus for Analytic Carleman Classes

1987
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Proceedings of the American Mathematical Society
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Let #M(/0) be the analytic Carleman class of ^-functions / defined in a sector 1a => [z e C: |argz| < aw/2} U {0} (0 sg a < 1) and analytic in its interior such that \\fM\\x « C\"Mn (n > 0), C -C(f), \ = \(f). In this paper, we give necessary and sufficient conditions in order that ^M(la) be inverse-closed. As a corollary, we obtain a characterization of ^M(R+ ) as an inverse-closed algebra, thus establishing the converse of a theorem of Malliavin [4] for the half-line.

doi:10.2307/2046638
fatcat:5oxuyyjbujcjfpykg26htjrbxy