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arXiv · 1712.01613

Weighted vector-valued functions and the $\varepsilon$-product

Karsten Kruse
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Abstract

We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth, holomorphic or harmonic functions. Then we exploit the construction of $\mathcal{FV}(\Omega,E)$ to derive sufficient conditions such that $\mathcal{FV}(\Omega,E)$ can be linearised, i.e. that $\mathcal{FV}(\Omega,E)$ is topologically isomorphic to the $\varepsilon$-product $\mathcal{FV}(\Omega)\varepsilon E$ where $\mathcal{FV}(\Omega):=\mathcal{FV}(\Omega,\mathbb{K})$ and $\mathbb{K}$ is the scalar field of $E$.

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Karsten Kruse. 2017-12-05. Weighted vector-valued functions and the $\varepsilon$-product. https://doi.org/10.1007/s43037-020-00072-z

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