Kruse, KarstenKarstenKruse2021-11-152021-11-152023-01Collectanea Mathematica 74 (1): 81-112 (2023-01)http://hdl.handle.net/11420/10923This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator ∂¯ on spaces EV(Ω, E) of C∞-smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights V. Vector-valued means that these functions have values in a locally convex Hausdorff space E over C. We derive a counterpart of the Grothendieck-Köthe-Silva duality O(C\ K) / O(C) ≅ A(K) with non-empty compact K⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of ∂¯ : EV(Ω, E) → EV(Ω, E) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on EV(Ω, C).en2038-48152023181112Springerhttps://creativecommons.org/licenses/by/4.0/Cauchy-RiemannParameter dependenceSmoothSolvabilityVector-valuedWeightMathematikJournal Article10.15480/882.389310.1007/s13348-021-00337-210.15480/882.38931901.02093Other