Interpolation of Vector‐Valued Real Analytic Functions

Let ω ⊆ R d be an open domain. The sequentially complete DF‐spaces E are characterized such that for each (some) discrete sequence ( z n ) ⊆ ω, a sequence of natural numbers ( k n ) and any family( X n , α)n ∈ N , | α | ⩽ k n⊆ E the infinite system of equations(∂ | α |f ∂ z α) ( z n ) = x n , αfor     n ∈ N , α ∈ N d , | α | ⩽ k n ,has an E ‐valued real analytic solution f .