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2 results

  • Universal Series on a Riemann Surface

  • Raphäel Clouâtre
  • Journal:
    Canadian Journal of Mathematics / Volume 63 / Issue 5 / 18 October 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 1025-1037
    Print publication:
    18 October 2011
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  • Every holomorphic function on a compact subset of a Riemann surface can be uniformly approximated by partial sums of a given series of functions. Those functions behave locally like the classical fundamental solutions of the Cauchy–Riemann operator in the plane.

  • On Weighted Polynomial Approximation With Gaps

  • Guantie Deng
  • Journal:
    Nagoya Mathematical Journal / Volume 178 / 2005
    Published online by Cambridge University Press:
    11 January 2016, pp. 55-61
    Print publication:
    2005
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  • Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.