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An extremal problem for polynomials with a pescribed value at a given point of the real axis. (English) Zbl 0686.30001

Let \(\rho\in {\mathbb{R}}\), \(\delta\geq 0\), \(n\in {\mathbb{N}}\) and \({\mathcal P}_ n(\rho,\delta)\) be the class of polynomials P of degree \(\leq n\) fulfilling \(P(\rho)=\delta\) and \(\max \{| P(e^{i\phi})|:\) \(\phi \in {\mathbb{R}}\}=1\). In this paper max\(\{\) \(| P(1)|:\) \(P\in {\mathcal P}_ n(\rho,\delta)\}\) is determined using a method which was found by St. Ruscheweyh and the author [comp.: J. Approximation Theory Appl. 1, No.3, 115-125 (1985; Zbl 0602.41005)].
Reviewer: K.-J.Wirths

MSC:

30C10 Polynomials and rational functions of one complex variable

Citations:

Zbl 0602.41005
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