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Title

A-differentiability and A-analyticity

AuthorsGadea, Pedro M. CSIC; Muñoz Masqué, Jaime
KeywordsFinite-dimensional commutative algebra over R
A-differentiable functions
A-analytic functions
Issue DateMay-1996
PublisherAmerican Mathematical Society
CitationProceedings of the American Mathematical Society 124(5): 1437–1443 (1996)
AbstractLet $A$ be a finite-dimensional commutative algebra over $\mathbb{R}$ and let $C_{A}^{r}(U)$, $C^{\omega}(U,A)$ and ${\cal O}_{A}(U)$ be the ring of $A$-differentiable functions of class $C^{r},\,0 \leq r \leq \infty$, the ring of real analytic mappings with values in $A$ and the ring of $A$-analytic functions, respectively, defined on an open subset $U$ of $A^{n}$. We prove two basic results concerning $A$-differentiability and $A$-analyticity: $1^{st}$) ${\cal O}_{A}(U) = C^{\infty}_{A}(U) \bigcap C^{\omega}(U,A)$, $2^{nd}$) ${\cal O}_{A}(U) = C^{\infty}_{A}(U)$ if and only if $A$ is defined over $\mathbb{C}$.
Description7 pages.-- MSC1991 codes: Primary 30G35; Secondary 26E05, 26E10, 16P10.
Publisher version (URL)http://www.ams.org/proc/1996-124-05/S0002-9939-96-03070-5/home.html
URIhttp://hdl.handle.net/10261/15786
ISSN0002-9939
E-ISSN1088-6826
Appears in Collections:(IFA) Artículos
(CFMAC-IFF) Artículos

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