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arXiv · 1309.6292

A Fundamental System of Seminorms for $A(K)$

Dietmar Vogt
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Abstract

Let $K\subset\R^d$ be compact and $A(K)$ the space of germs of real analytic functions on $K$ with its natural (LF)-topology. This topology can be given by $A(K)=\limind_{k\to+\infty} A_k$ where $A_k=\{(f_α)_{α\in\N_0^d}\in C(K)^{\N_0^d}\,:\, \|f\|_k:=\sup_{x\in K} \frac{|f^{(α)}(x)|}{α!} k^{-|α|}< +\infty\}.$ Based on this description we give in the present note an explicit fundamental system of seminorms for $A(K)$.

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Dietmar Vogt. 2013-09-23. A Fundamental System of Seminorms for $A(K)$. https://arxiv.org/abs/1309.6292

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