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<p>We study angular weighted spaces of holomorphic functions in the polydisk and in the unit ball. We seek for Mergelyan-type conditions on the weights to ensure that the dilations of a given function converge to the same function in norm. This, in turn, leads to the approximation of functions in these spaces by analytic polynomials.</p>

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Approximation in Holomorphic Spaces with Angular Weights

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Ali Abkar

摘要

We study angular weighted spaces of holomorphic functions in the polydisk and in the unit ball. We seek for Mergelyan-type conditions on the weights to ensure that the dilations of a given function converge to the same function in norm. This, in turn, leads to the approximation of functions in these spaces by analytic polynomials.