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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the distribution of extremal points of general Chebyshev polynomials


Authors: András Kroó and Franz Peherstorfer
Journal: Trans. Amer. Math. Soc. 329 (1992), 117-130
MSC: Primary 41A50; Secondary 41A30
MathSciNet review: 1012514
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Abstract: For a linear subspace $ {\mathcal{U}_n} = {\operatorname{span}}[{\varphi _1}, \ldots ,{\varphi _n}]$ in $ C[a,b]$ we introduce general Chebyshev polynomials as solutions of the minimization problem $ {\operatorname{min}_{{a_i}}}{\left\Vert {{\varphi _n} - \sum\nolimits_{i = 1}^{n - 1} {{a_i}{\varphi _i}} } \right\Vert _C}$. For such a Chebyshev polynomial we study the distribution of its extremal points (maximum and minimum points) in terms of structural and approximative properties of $ {\mathcal{U}_n}$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1012514-4
Keywords: Chebyshev polynomials, density of extremal points
Article copyright: © Copyright 1992 American Mathematical Society