The structure of spaces of quasianalytic functions of Roumieu type

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• 作者：Jos¨¦ Bonet and Pawel Doma¨½ski
• 关键词：Splitting of short exact sequences ; space of real analytic functions ; space of ultradifferentiable functions of Roumieu type ; functor Ext1 ; PLS ; space ; locally convex space ; Fr¨¦chet space ; linear partial differential operator ; convolution operator
• 刊名：Archiv der Mathematik
• 出版年：2007
• 出版时间：November, 2007
• 年：2007
• 卷：89
• 期：5
• 页码：430-441
• 全文大小：186.4 KB

文摘

It is shown that spaces of quasianalytic ultradifferentiable functions of Roumieu type ℰ_{w}(Ω), on an open convex set (W) ¨ª \mathbbRd(\Omega)\,{\subseteq}\,{\mathbb{R}}^d, satisfy some new (Ω) -type linear topological invariants. Some consequences for the splitting of short exact sequences of these spaces as well as for the structure of the spaces are derived. In particular, Fr¨¦chet quotients of ℰ_{w}(Ω) have property ([`([`(W)])]\overline{\overline \Omega}), while dual Fr¨¦chet quotients have property (A\underline{A}) of Vogt.