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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weighted-$L^2$ polynomial approximation in $\mathbb {C}$
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by Séverine Biard, John Erik Fornæss and Jujie Wu PDF
Trans. Amer. Math. Soc. 373 (2020), 919-938 Request permission

Abstract:

We study the density of polynomials in $H^2(\Omega ,e^{-\varphi })$, the space of square integrable holomorphic functions in a bounded domain $\Omega$ in $\mathbb {C}$, where $\varphi$ is a subharmonic function. In particular, we prove that the density holds in Carathéodory domains for any subharmonic function $\varphi$ in a neighborhood of $\overline {\Omega }$. In non-Carathéodory domains, we prove that the density depends on the weight function, giving examples.
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Additional Information
  • Séverine Biard
  • Affiliation: Science Institute, University of Iceland, Dunhagi 3, IS-107 Reykjavik, Iceland
  • Email: biard@hi.is
  • John Erik Fornæss
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg 2, Alfred Getz vei 1, 7034 Trondheim, Norway
  • Address at time of publication: LAMAV, Université polytechnique Hauts-de-France, Campus du Mont d’Houy, 59313 Valenciennes Cedex 9, France
  • MR Author ID: 68145
  • Email: severine.biard@uphf.fr
  • Jujie Wu
  • Affiliation: School of Mathematics and Statistics, Henan University, Kaifeng 475001, Henan Province, People’s Republic of China; and Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg 2, Alfred Getz vei 1, 7034 Trondheim, Norway
  • MR Author ID: 1249622
  • Email: jujie.wu@ntnu.no, 99jujiewu@tongji.edu.cn
  • Received by editor(s): June 19, 2018
  • Received by editor(s) in revised form: February 27, 2019
  • Published electronically: October 28, 2019
  • Additional Notes: The first author was supported in part by Rannis-grant 152572-051
    The second author was supported by the Norwegian Research Council grant 240569
    The third author was supported by the Norwegian Research Council grant 240569 and NSFC grant 11601120. The third author is the corresponding author
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 919-938
  • MSC (2010): Primary 30B60, 30E10; Secondary 32A10, 32E30, 32W05, 31A05
  • DOI: https://doi.org/10.1090/tran/7935
  • MathSciNet review: 4068254