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Inverse-closed Carleman algebras of infinitely differentiable functions


Author: Jamil A. Siddiqi
Journal: Proc. Amer. Math. Soc. 109 (1990), 357-367
MSC: Primary 46J15; Secondary 30D60, 46E25
DOI: https://doi.org/10.1090/S0002-9939-1990-1007512-4
MathSciNet review: 1007512
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Abstract: We characterize the classes $ {\mathcal{C}_M}(I)$ and $ \mathcal{C}_M^ * (I)$ of infinitely differentiable functions which are inverse-closed thereby giving a complete solution to a problem first posed by W. Rudin [11] and solved by him and J. Boman and L. Hörmander [2] for classes $ {\mathcal{C}_M}({\mathbf{R}})$ alone.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1007512-4
Keywords: Carleman and local Carleman classes, inverse-closed algebras, log-convex sequences, almost increasing sequences
Article copyright: © Copyright 1990 American Mathematical Society

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