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Pointwise bounded approximation by polynomials

Published online by Cambridge University Press:  24 October 2008

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

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 ∥f∥A:

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 147 - 155
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Fisher, S. D.. Function Theory on Planar Domains (John Wiley & Sons, 1983).Google Scholar
[2]Gamelin, T. W.. Uniform Algebras (Prentice-Hall, 1969).Google Scholar
[3]Makarov, N. O.. On the distortion of the boundary sets under conformal mapping. Proc. London Math. Soc. (3) 51 (1985), 369–384.CrossRefGoogle Scholar
[4]Stray, A.. Pointwise bounded approximation by functions satisfying a side condition. Pacific J. Math. 51 (1974), 301–305.CrossRefGoogle Scholar