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Pointwise bounded approximation by polynomials

  • Anthony G. O'Farrell (a1) and Fernando Perez-Gonzalez (a2)
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For a bounded open set U ⊂ ℂ, we denote by H(U) the collection of all bounded analytic functions on U. We let X denote bdy (U), the boundary of U, Y denote the polynomial hull of U (the complement of the unbounded component of ℂ / X), and U* denote mt (Y), the interior of Y. We denote the sup norm of a function f: A → ℂ by ∥fA:

We denote the space of all analytic polynomials by ℂ[z], and we denote the open unit disc by D and the unit circle by S1.

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[1]Fisher, S. D.. Function Theory on Planar Domains (John Wiley & Sons, 1983).
[2]Gamelin, T. W.. Uniform Algebras (Prentice-Hall, 1969).
[3]Makarov, N. O.. On the distortion of the boundary sets under conformal mapping. Proc. London Math. Soc. (3) 51 (1985), 369384.
[4]Stray, A.. Pointwise bounded approximation by functions satisfying a side condition. Pacific J. Math. 51 (1974), 301305.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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