2019
DOI: 10.48550/arxiv.1901.02093
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The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes

Karsten Kruse

Abstract: This 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 characterise the weights V which give a counterpart of the Grothendieck-Köthe-Silva duality O(C ∖ K) O(C) ≅ A (K) with non-empty compact K ⊂ R for weighted holomorp… Show more

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