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The sequential stability index of a function space
Published online by Cambridge University Press: 26 February 2010
Extract
One of the substantial differences between real and complex analysis is the behaviour of pointwise sequential limits of functions. It is well known that, if f(z) is a bounded analytic function in D = {z∈ C: |z| < 1}, then there exists a sequence {pn(z): n = 1,2,…} of polynomials such that
(i) ‖Pn‖ ≤ ‖f‖ for all n = 1,2,3,…, and
(ii) for each z ∈ D, Pn(Z) → f(z) as n → ∞,
where we have used the notation
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- Research Article
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- Copyright © University College London 1973
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