### Analytic curves in power series rings

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Let (U) denote the algebra of holomorphic functions on an open subset U ⊂ ℂⁿ and Z ⊂ (U) its finite-dimensional vector subspace. By the theory of least spaces of de Boor and Ron, there exists a projection ${}_{b}$ from the local ring ${}_{n,b}$ onto the space ${Z}_{b}$ of germs of elements of Z at b. At a general point b ∈ U its kernel is an ideal and ${}_{b}$ induces the structure of an Artinian algebra on ${Z}_{b}$. In particular, this holds at points where the kth jets of elements of Z form a vector bundle for each k ∈ ℕ. For an embedded...