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arXiv · 1201.2938

Inverse Closed Ultradifferential Subalgebras

Andreas Klotz
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Abstract

In previous work we have shown that classical approximation theory provides methods for the systematic construction of inverse-closed smooth subalgebras. Now we extend this work to treat inverse-closed subalgebras of ultradifferentiable elements. In particular, Carleman classes and Dales-Davie algebras are treated. As an application the result of Demko, Smith and Moss and Jaffard on the inverse of a matrix with exponential decay is obtained within the framework of a general theory of smoothness.

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Andreas Klotz. 2012-01-13. Inverse Closed Ultradifferential Subalgebras. https://arxiv.org/abs/1201.2938

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