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Published in:
2014 | OriginalPaper | Chapter
13. Maximal Polynomial Ranges for a Domain of Intersection of Two Circular Disks
Author : Chinta Mani Pokhrel
Published in: Current Topics in Pure and Computational Complex Analysis
Publisher: Springer India
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Abstract
Let Ω be a domain in the complex plane \(\mathbb{C}\) containing the origin and let \({\cal P}_{n}^{0}(\Omega)\) denote the set of all polynomials P of degree ≤ n satisfying the conditions \(P(0)=0\) and \(P(\mathbb{D})\subset \Omega\), where \(\mathbb{D}=\left\{z\,:\,\,|z|<1\right\}\) is the unit disk in the complex plane. The maximal range, denoted by Ω
n
, is then defined as the union of all sets \(P(\mathbb{D}), P \in {\cal P}_{n}^{0}\) .We shall construct extremal polynomials and maximal polynomial range for a domain of intersection of two circular disks.