Pointwise bounded approximation by polynomials
Published online by Cambridge University Press: 24 October 2008
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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