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2 results

  • UNIVERSAL LAURENT SERIES

  • G. Costakis, V. Nestoridis, I. Papadoperakis
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 48 / Issue 3 / October 2005
    Published online by Cambridge University Press:
    15 September 2005, pp. 571-583
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  • Universal Taylor series are defined on simply connected domains, but they do not exist on an annulus. Instead we introduce universal Laurent or Laurent–Faber series on finitely connected domains in $\mathbb{C}$. These are generic universalities. Furthermore, we study some properties of universal Laurent series on an annulus.

  • SP Transform and Uniform Convergence of Laurent and Power Series

  • S.A. Settu
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 1 / 01 March 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 114-123
    Print publication:
    01 March 1987
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  • If the Laurent series

    is transformed to

    it is shown that convergence of the former at z = 1 implies the uniform convergence of the latter on a symmetric arc of |z - 1/P| = 1/P - 1 not containing z = 1 and that the uniform convergence of the former over a symmetric arc of |z| = 1 containing z = 1 implies uniform convergence of the latter on the entire circle |z — 1/P| = 1/P — 1.