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A Fundamental System of Seminorms for $A(K)$ | | Dietmar Vogt
; | | Date: |
23 Sep 2013 | | Abstract: | Let $KsubsetR^d$ 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
$A(K)=limind_{k o+infty} A_k$ where $A_k={(f_alpha)_{alphainN_0^d}in
C(K)^{N_0^d},:, |f|_k:=sup_{xin K} frac{|f^{(alpha)}(x)|}{alpha!}
k^{-|alpha|}< +infty}.$ Based on this description we give in the present
note an explicit fundamental system of seminorms for $A(K)$. | | Source: | arXiv, 1309.6292 | | Services: | Forum | Review | PDF | Favorites | |
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