Coefficient multipliers for polynomials (Q2764276)
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scientific article; zbMATH DE number 1690298
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Coefficient multipliers for polynomials |
scientific article; zbMATH DE number 1690298 |
Statements
28 July 2002
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Hadamard products
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geometry of polynomials
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0.8793702
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0.87931234
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0.8748808
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0.87460285
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0.87294525
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0.87037957
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Coefficient multipliers for polynomials (English)
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Let \(Q_n\) denote the class of all polynomials \(p(z)\) nonvanishing in the unit disk with \(\deg p\leq n\) and \(p(0)=1\), and let \(W_n\) denote the class of all polynomials \(s(z)\) satisfying \(\deg s\leq n\) and for all \(p\in Q_n\), \(s^*p\in Q_n\), where \(^*\) denotes the Hadamard product. Certain properties of \(W_n\) and \(Q_n\) are obtained. The results obtained and techniques used are either contained in or closely related to the Duality Principle and its applications as presented in [\textit{St. Ruscheweyh} ``Convolutions in geometric function theory'' (1982; Zbl 0499.30001), 166 p.].
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