Weighted L^2 Version of Mergelyan and Carleman Approximation

Journal of Geometric Analysis(2020)

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摘要
We study the density of polynomials in H^2(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 L^2 -version of the Mergelyan theorem. We also prove a weighted L^2 -version of the Carleman theorem.
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关键词
carleman approximation,mergelyan
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