Polynomial approximation in weighted Dirichlet spaces


We give an elementary proof of an analogue of Fejér’s theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.

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JM supported by an NSERC grant. TR supported by grants from NSERC and the Canada Research Chairs program.

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Correspondence to Thomas Ransford.

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Mashreghi, J., Ransford, T. Polynomial approximation in weighted Dirichlet spaces. Complex Anal Synerg 7, 11 (2021). https://doi.org/10.1007/s40627-021-00078-9

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  • Dirichlet space
  • Superharmonic weight
  • Fejér theorem

Mathematics Subject Classification

  • 41A10
  • 30E10
  • 30H99