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Weighted approximation in \(\mathbb {C}\)

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Abstract

We prove that if \(\{ \varphi _j\}_j\) is a sequence of subharmonic functions which are increasing to some subharmonic function \(\varphi \) in \(\mathbb {C}\), then the union of all the weighted Hilbert spaces \(H(\varphi _j)\) is dense in the weighted Hilbert space \(H(\varphi )\).

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Acknowledgements

The authors would thank the referee for his/her helpful comments and suggestions. The authors were supported in part by the Norwegian Research Council Grant number 240569, the first author was also supported by NSFC Grant 11601120. The first author also thanks Professor Bo-Yong Chen for his valuable comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University, Kaifeng, 475001, Henan, People’s Republic of China

    Jujie Wu

  2. Department of Mathematical Sciences, NTNU, Sentralbygg 2, Alfred Getz vei 1, 7034, Trondheim, Norway

    John Erik Fornæss & Jujie Wu

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  1. John Erik Fornæss
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  2. Jujie Wu
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Correspondence to Jujie Wu.

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Fornæss, J.E., Wu, J. Weighted approximation in \(\mathbb {C}\). Math. Z. 294, 1051–1064 (2020). https://doi.org/10.1007/s00209-019-02321-w

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  • DOI: https://doi.org/10.1007/s00209-019-02321-w

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