𝐴-differentiability and 𝐴-analyticity
P. M. Gadea, J. Munñoz Masqué · Proceedings of the American Mathematical Society · 1996
Let A A be a finite-dimensional commutative algebra over R \mathbb {R} and let C A r ( U ) C_{A}^{r}(U) , C ω ( U , A ) C^{\omega }(U,A) and O A ( U ) \mathcal { O}_{A}(U) be the ring of A A -differentiable functions of class C r , 0 ≤ r ≤ ∞ C^{r},\,0 \leq r \leq \infty , the ring of real analytic mappings with values in A A and the ring of A A -analytic functions, respectively, defined on an open subset U U of A n A^{n} . We prove two basic results concerning A A -differentiability and A