Journal Articles The Journal of Geometric Analysis Year : 2021

Weighted $$L^2$$ Version of Mergelyan and Carleman Approximation

Abstract

Abstract We study the density of polynomials in H2 ( E , φ ) , the space of square integrable functions with respect to e−φdm and holomorphic on the interior of E in C, where φ is a subharmonic function and d m is a measure on E . We give a result where E is the union of a Lipschitz graph and a Carathéodory domain, which we state as a weighted L2-version of the Mergelyan theorem. We also prove a weighted L 2 -version of the Carleman theorem.

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hal-03207775 , version 1 (06-07-2022)

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Séverine Biard, John Erik Fornæss, Jujie Wu. Weighted $$L^2$$ Version of Mergelyan and Carleman Approximation. The Journal of Geometric Analysis, 2021, 31 (4), pp.3889-3914. ⟨10.1007/s12220-020-00418-x⟩. ⟨hal-03207775⟩
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