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The extreme points of some classes of polynomials
Published online by Cambridge University Press: 14 November 2011
Synopsis
We study the extreme points of two classes of polynomials of degree at most n:
It turns out that f ∈ Ext if and only if Re f(eiθ) has exactly 2n zeros in [0, 2π). On the other hand, if f∈Hn and 1−|f(eiθ)|2 has 2n zeros in [0, 2π), then either f ∈ Ext Hn or else f(z) = α + βzn where |α|+|β| = l and αβ≠0; if 1−|f(eiθ)|2 has 2m zeros, 2n, then f may or may not belong to Ext Hn.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 99 - 110
- Copyright
- Copyright © Royal Society of Edinburgh 1985
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