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Weighted spaces of harmonic and holomorphic functions: Sequence space representations and projective descriptions. (English) Zbl 0898.46022
Summary: We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of \(\mathbb{C}\), and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk \(D\) of \(\mathbb{C}\), that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on \(D\). We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on \(D\) are isomorphic to corresponding spaces of continuous or bounded functions on \(\partial D\).

MSC:
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46E15 Banach spaces of continuous, differentiable or analytic functions
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