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For v\in R^n let K be a compact set in R^n containing a suitable smoothsurface and such that the intersection {tv+x:t\in R}\cap K is a closed intervalor a single point for all x\in K. We prove that every linear first orderdifferential operator with constant coefficients in direction v on space ofWhitney functions E(K) admits a continuous linear right inverse.

Right inverses for partial differential operators on spaces of Whitney functions