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Pointwise bounded approximation by polynomials

Published online by Cambridge University Press:  24 October 2008

Anthony G. O'Farrell
Maynooth College, Co. Kildare, Ireland
Fernando Perez-Gonzalez
Department de Análysis Matemático, CIMAC, Universidad de la Laguna, 38271 La Laguna, Tenerife, Canary islands, Spain


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.

Research Article
Copyright © Cambridge Philosophical Society 1992

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